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Texas Instruments TI-82 Manual

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8200$FNT.DOC TI-82, Front Matter, English Bob Fedorisko Revised: 02/09/01 12:16 PM Printed:
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8200$FNT.DOC TI-82, Front Matter, English Bob Fedorisko Revised: 02/09/01 12:16 PM Printed:
02/09/01 1:12 PM Page 1 of 10
TI
-
82
GRAPHING CALCULATOR
GUIDEBOOK
TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger,
CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of
Texas Instruments Incorporated.
Macintosh is a registered trademark of Apple Computer, Inc.
© 1993, 2000, 2001 Texas Instruments Incorporated.
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Important
Texas Instruments makes no warranty, either expressed or implied,
including but not limited to any implied warranties of merchantability and
fitness for a particular purpose, regarding any programs or book materials
and makes such materials available solely on an “as-is” basis.
In no event shall Texas Instruments be liable to anyone for special,
collateral, incidental, or consequential damages in connection with or
arising out of the purchase or use of these materials, and the sole and
exclusive liability of Texas Instruments, regardless of the form of action,
shall not exceed the purchase price of this equipment. Moreover, Texas
Instruments shall not be liable for any claim of any kind whatsoever against
the use of these materials by any other party.
US FCC Information Concerning Radio Frequency Interference
This equipment has been tested and found to comply with the limits for a Class
B digital device, pursuant to Part 15 of the FCC rules. These limits are designed
to provide reasonable protection against harmful interference in a residential
installation. This equipment generates, uses, and can radiate radio frequency
energy and, if not installed and used in accordance with the instructions, may
cause harmful interference with radio communications. However, there is no
guarantee that interference will not occur in a particular installation.
If this equipment does cause harmful interference to radio or television
reception, which can be determined by turning the equipment off and on, you
can try to correct the interference by one or more of the following measures:
•
Reorient or relocate the receiving antenna.
•
Increase the separation between the equipment and receiver.
•
Connect the equipment into an outlet on a circuit different from that to
which the receiver is connected.
•
Consult the dealer or an experienced radio/television technician for help.
Caution:
Any changes or modifications to this equipment not expressly
approved by Texas Instruments may void your authority to operate the
equipment.
Introduction iii
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Table of Contents
This manual describes how to use the TI
.
82 Graphing Calculator. Getting Started
gives a quick overview of its features. The first chapter gives general instructions
on operating the TI
.
82. Other chapters describe its interactive features. The
applications in Chapter 14 show how to use these features together.
Using this Guidebook Effectively
...................
viii
Glossary
.....................................
x
Getting Started: Do This First!
TI
.
82 Menus
..................................
2
First Steps
...................................
3
Entering a Calculation: Compound Interest
............
4
Defining a Function: Box with Lid
..................
6
Defining a Table of Values
........................
7
Zooming In on the Table
..........................
8
Changing the Viewing
WINDOW
....................
10
Displaying and Tracing the Graph
...................
11
Zooming In on the Graph
.........................
12
Finding the Calculated Maximum
...................
13
Other Features
................................
14
Chapter 1: Operating the TI
.
82
Turning the TI
.
82 On and Off
......................
1-2
Setting the Display Contrast
.......................
1-3
The Display
..................................
1-4
Entering Expressions and Instructions
...............
1-6
TI
.
82 Edit Keys
................................
1-8
Setting Modes
.................................
1-9
TI
.
82 Modes
..................................
1-10
Variable Names
................................
1-12
Storing and Recalling Variable Values
................
1-13
Last Entry
....................................
1-14
Last Answer
..................................
1-16
TI
.
82 Menus
..................................
1-17
VARS
and
Y-VARS
Menus
........................
1-19
EOS
é
(Equation Operating System)
.................
1-20
Error Conditions
...............................
1-22
iv Introduction
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Chapter 2: Math, Angle, and Test Operations
Getting Started: Lottery Chances
...................
2-2
Keyboard Math Operations
.......................
2-3
MATH MATH
Operations
.........................
2-5
MATH NUM
(Number) Operations
..................
2-9
MATH HYP
(Hyperbolic) Operations
.................
2-11
MATH PRB
(Probability) Operations
.................
2-12
ANGLE
Operations
.............................
2-13
TEST TEST
(Relational) Operations
.................
2-15
TEST LOGIC
(Boolean) Operations
.................
2-16
Chapter 3: Function Graphing
Getting Started: Graphing a Circle
..................
3-2
Defining a Graph
...............................
3-3
Setting Graph Modes
............................
3-4
Defining Functions in the
Y=
List
...................
3-5
Selecting Functions
.............................
3-7
Defining the Viewing
WINDOW
....................
3-8
Setting
WINDOW FORMAT
........................
3-10
Displaying a Graph
.............................
3-11
Exploring a Graph with the Free-Moving Cursor
........
3-13
Exploring a Graph with
TRACE
....................
3-14
Exploring a Graph with
ZOOM
.....................
3-16
Using
ZOOM MEMORY
..........................
3-19
Setting
ZOOM FACTORS
.........................
3-21
Using
CALC
(Calculate) Operations
.................
3-22
Chapter 4: Parametric Graphing
Getting Started: Path of a Ball
.....................
4-2
Defining and Displaying a Parametric Graph
...........
4-3
Exploring a Parametric Graph
.....................
4-6
Chapter 5: Polar Graphing
Getting Started: Polar Rose
.......................
5-2
Defining and Displaying a Polar Graph
...............
5-3
Exploring a Polar Graph
.........................
5-6
Introduction v
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Chapter 6: Sequence Graphing
Getting Started: Forest and Trees
...................
6-2
Defining and Displaying a Sequence Graph
............
6-3
Exploring a Sequence Graph
......................
6-6
Chapter 7: Tables
Getting Started: Roots of a Function
.................
7-2
Defining the Variables
...........................
7-3
Defining the Dependent Variable
...................
7-4
Displaying the Table
............................
7-5
Chapter 8: DRAW Operations
Getting Started: Shading a Graph
...................
8-2
DRAW DRAW
Menu
............................
8-3
Drawing Lines
................................
8-4
Drawing Horizontal and Vertical Lines
...............
8-5
Drawing Tangent Lines
..........................
8-6
Drawing Functions and Inverses
...................
8-7
Shading Areas on a Graph
........................
8-8
Drawing Circles
...............................
8-9
Placing Text on a Graph
.........................
8-10
Using
Pen
to Draw on a Graph
.....................
8-11
Drawing Points
................................
8-12
Drawing Pixels
................................
8-13
Storing and Recalling Graph Pictures
................
8-14
Storing and Recalling Graph Databases
...............
8-15
Clearing a Drawing
.............................
8-16
Chapter 9: Split Screen
Getting Started: Polynomial Coefficients
..............
9-2
Using Split Screen
..............................
9-3
vi Introduction
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Chapter 10: Matrices
Getting Started: Systems of Linear Equations
..........
10-2
Defining a Matrix
..............................
10-4
Viewing Matrix Elements
.........................
10-5
Editing Matrix Elements
.........................
10-6
About Matrices
................................
10-8
Matrix Math Functions
..........................
10-10
MATRIX MATH
Operations
........................
10-12
Chapter 11: Lists
Getting Started: Generating Sequences
...............
11-2
About Lists
...................................
11-3
LIST OPS
Operations
...........................
11-6
LIST MATH
Operations
..........................
11-9
Chapter 12: Statistics
Getting Started: Building Height and City Size
..........
12-2
Setting Up a Statistical Analysis
....................
12-9
Viewing List Elements
...........................
12-10
Editing List Elements
...........................
12-11
STAT EDIT
Menu
...............................
12-12
Statistical Analysis
.............................
12-13
Statistical Variables
.............................
12-14
Types of Statistical Analysis
.......................
12-15
Statistical Analysis in a Program
...................
12-17
Statistical Plotting
..............................
12-18
Statistical Plotting in a Program
....................
12-22
Chapter 13: Programming
Getting Started: Family of Curves
...................
13-2
About Programs
...............................
13-4
Creating and Executing Programs
..................
13-5
Editing Programs
..............................
13-6
PRGM CTL
(Control) Instructions
..................
13-7
PRGM I/O
(Input/Output) Instructions
...............
13-15
Calling Other Programs
..........................
13-18
Introduction vii
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Chapter 14: Applications
Left-Brain, Right-Brain Test Results
.................
14-2
Speeding Tickets
...............................
14-4
Buying a Car, Now or Later?
......................
14-5
Graphing Inequalities
...........................
14-6
Solving a System of Nonlinear Equations
.............
14-7
Program: Sierpinski Triangle
......................
14-8
Cobweb Attractors
.............................
14-9
Program: Guess the Coefficients
...................
14-10
The Unit Circle and Trigonometric Curves
............
14-11
Ferris Wheel Problem
...........................
14-12
Reservoir Problem
.............................
14-14
Predator-Prey Model
............................
14-16
Fundamental Theorem of Calculus
..................
14-18
Finding the Area between Curves
...................
14-20
Chapter 15: Memory Management
Checking Available Memory
.......................
15-2
Deleting Items from Memory
......................
15-3
Resetting the TI
.
82
.............................
15-4
Chapter 16: Communication Link
Getting Started: Sending Variables
..................
16-2
TI
.
82
LINK
...................................
16-3
Selecting Items to Send
..........................
16-4
Transmitting Items
.............................
16-6
Receiving Items
...............................
16-7
Backing Up Memory
............................
16-8
Appendix A: Tables
Tables of Functions and Instructions
................
A-2
Menu Map
...................................
A-22
Table of System Variables
........................
A-28
Appendix B: Reference Information
Battery Information
.............................
B-2
In Case of Difficulty
............................
B-4
Accuracy Information
...........................
B-5
Error Conditions
...............................
B-7
Service and Support Information
...................
B-11
Warranty Information
...........................
B-12
Index
viii Introduction
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Using this Guidebook Effectively
The structure of the TI
.
82 guidebook and the design of its pages can help you
find the information you need quickly. Consistent presentation techniques are
used throughout to make the guidebook easy to use.
Structure of the Guidebook
The guidebook contains sections that teach you how to use the calculator.
¦
Getting Started is a fast-paced keystroke-by-keystroke introduction.
¦
Chapter 1 describes general operation and lays the foundation for
Chapters 2 through 13, which describe specific functional areas of the
TI
.
82. Each begins with a brief Getting Started introduction.
¦
Chapter 14 contains application examples that incorporate features
from different functional areas of the calculator. These examples can
help you see how different functional areas work together to
accomplish meaningful tasks.
¦
Chapter 15 describes memory management and Chapter 16 describes
the communications link.
Page-Design Conventions
When possible, units of information are presented on a single page or on
two facing pages. Several page-design elements help you find information
quickly.
¦
Page headings—The descriptive heading at the top of the page or two-
page unit identifies the subject of the unit.
¦
General text—Just below the page heading, a short section of bold
text provides general information about the subject covered in the unit.
¦
Left-column subheadings—Each subheading identifies a specific
topic or task related to the page or unit subject.
¦
Specific text—The text to the right of a subheading presents detailed
information about that specific topic or task. The information may be
presented as paragraphs, numbered procedures, bulleted lists, or
illustrations.
¦
Page “footers”—The bottom of each page shows the chapter name,
chapter number, and page number.
Introduction ix
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Information-Mapping Conventions
Several conventions are used to present information concisely and in an
easily referenced format.
¦
Numbered procedures—A procedure is a sequence of steps that
performs a task. In this guidebook, each step is numbered in the order
in which it is performed. No other text in the guidebook is numbered;
therefore, when you see numbered text, you know you must perform
the steps sequentially.
¦
“Bulleted” lists—If several items have equal importance, or if you
may choose one of several alternative actions, this guidebook precedes
each item with a “bullet” (
¦
) to highlight it—like this list.
¦
Tables and charts—Sets of related information are presented in tables
or charts for quick reference.
¦
Keystroke Examples—The Getting Started examples provide
keystroke-by-keystroke instructions, as do examples identified with a
.
Reference Aids
Several techniques have been used to help you look up specific information
when you need it. These include:
¦
A chapter table of contents on the first page of each chapter, as well as
the full table of contents at the front of the guidebook.
¦
A glossary at the end of this section, defining important terms used
throughout the guidebook.
¦
An alphabetical table of functions and instructions in Appendix A,
showing their correct formats, how to access them, and page references
for more information.
¦
Information about system variables in Appendix A.
¦
A table of error messages in Appendix B, showing the messages and
their meanings, with problem-handling information.
¦
An alphabetical index at the back of the guidebook, listing tasks and
topics you may need to look up.
x Introduction
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Glossary
This glossary provides definitions for important terms that are used throughout
this guidebook.
Expression
An expression is a complete sequence of numbers, variables,
functions, and their arguments that can be evaluated to a single
answer.
Function
A function, which may have arguments, returns a value and can
be used in an expression.
A function is also the expression entered in the
Y=
editor used
in graphing and
TABLE
.
Graph Database
A graph database is composed of the elements that define a
graph: functions in the
Y=
list,
MODE
settings, and
WINDOW
settings. They may be saved as a unit in a graph database to
recreate the graph later.
Graph Picture
A picture is a saved image of a graph display, excluding cursor
coordinates, axis labels, tick marks, and prompts. It may be
superimposed on another graph.
Home Screen
The Home Screen is the primary screen of the TI
.
82, where
expressions can be entered and evaluated and instructions can
be entered and executed.
Instruction
An instruction, which may have arguments, initiates an action.
Instructions are not valid in expressions.
List
A list is a set of values that the TI
.
82 can use for activities such
as graphing a family of curves, evaluating a function at multiple
v
alues, and entering statistical data.
Matrix
A matrix is a two-dimensional array on which the TI
.
82 can
perform operations.
Menu Items
Menu items are shown on full-screen menus.
Pixel
A pixel (picture element) is a square dot on the TI
.
82 display.
The TI
.
82 display is 96 pixels wide and 64 pixels high.
Variable
A variable is the name given to a location in memory in which a
v
alue, an expression, a list, a matrix, or another named item is
stored.
Getting Started 1
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Getting Started: Do This First!
Getting Started contains two keystroke-by-keystroke examples, an interest rate
problem and a volume problem, that introduce you to some principal operating
and graphing features of the TI
.
82. You will learn to use the TI
.
82 much more
quickly by completing both of these examples first.
Contents
TI
.
82 Menus
................................
2
First Steps
.................................
3
Entering a Calculation: Compound Interest
..........
4
Defining a Function: Box with Lid
................
6
Defining a Table of Values
......................
7
Zooming In on the Table
........................
8
Changing the Viewing
WINDOW
..................
10
Displaying and Tracing the Graph
.................
11
Zooming In on the Graph
.......................
12
Finding the Calculated Maximum
.................
13
Other Features
..............................
14
2 Getting Started
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TI-82 Menus
To leave the keyboard uncluttered, the TI
.
82 uses full-screen menus to access
many additional operations. The use of specific menus is described in the
appropriate chapters.
Displaying a Menu
When you press a key that accesses a menu, such
as
, that menu screen temporarily replaces the
screen where you are working.
A
fter you make a selection from a menu, you
usually are returned to the screen where you were.
Moving from One Menu to Another
A
menu key may access more than one menu. The
names of the menus appear on the top line. The
current menu is highlighted and the items in that
menu are displayed.
Use
~
or
|
to display a different menu.
Selecting an Item from a Menu
The number of the current item is highlighted. If
there are more than seven items on the menu, a
$
appears on the last line in place of the
:
(colon).
To select from a menu:
¦
Use
†
and
}
to move the cursor to the item
and then press
Í
.
¦
Press the number of the item.
Leaving without Making a Selection
To leave a menu without making a selection:
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
¦
Press
‘
to return to the screen where you
were.
¦
Select another screen or menu.
Getting Started 3
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First Steps
Before beginning these sample problems, follow the steps on this page to reset
the TI
.
82 to its factory settings. (Resetting the TI
.
82 erases all previously entered
data.) This ensures that following the keystrokes in this section produces the
illustrated actions.
1. Press
É
to turn the calculator on.
2. Press and release
y
and then press
Ã
.
(Pressing
y
accesses the operation printed in
blue to the left above the next key that you
press.
MEM
is the
2nd
operation of
Ã
.)
The
MEMORY
menu is displayed.
3. Press
3
to select
Reset...
.
The
RESET MEMORY
menu is displayed.
4. Press
2
to select
Reset
. The calculator is reset.
5. After a reset, the display contrast is also reset. If
the screen is very dark or blank, you need to
adjust the display contrast. Press
y
and then
press and hold
†
(to make the display lighter)
or
}
(to make the display darker). You can
press
‘
to clear the display.
4 Getting Started
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Entering a Calculation: Compound Interest
Using trial and error, determine when an amount invested at 6% annual
compounded interest will double in value. The TI
.
82 displays up to 8 lines of 16
characters so you see an expression and its solution at the same time. You also
can store values to variables, enter multiple instructions on one line, and recall
previous entries.
1. Press
.06
¿
ƒ
Z
(annual interest rate) to
store the interest rate.
2. Press
y
ã
:
ä
to enter more than one instruction
on a line.
3. For the first guess, compute the amount
available at the end of 10 years. Enter
10
¿
ƒ
Y
(years).
4. Press
y
ã
:
ä
, then enter the expression to
calculate the total amount available after
Y
years at
Z
interest just as you would write it. Use
1000 as the amount. Press
1000
¯
£
1
Ã
ƒ
Z
¤
›
ƒ
Y
.
The entire problem is shown in the first two
lines of the display.
5. Press
Í
to evaluate the expression.
The answer is shown on the right side of the
display. The cursor is positioned on the next
line, ready for you to enter the next expression.
6. To save keystrokes, you can use
Last Entry
to
recall the last expression entered and then edit
it for a new calculation. Press
y
, followed by
ã
ENTRY
ä
(above
Í
).
The last calculated expression is shown on the
next line of the display.
Getting Started 5
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7. The next guess should be greater than 10
years. Make the next guess 12 years. Press
}
to move the cursor over the
0
, and then type
2
to change
10
to
12
. Press
Í
to evaluate the
expression.
8. To display answers in a format more
appropriate for calculations involving money,
press
z
to display the
MODE
screen.
9. Press
†
~
~
~
to position the cursor over the
2 and then press
Í
. This changes the
display format to two fixed decimal places.
10. Press
y
ã
QUIT
ä
(above
z
) to return to the
Home screen. The next guess should be less
than, but close to, 12 years. Press
y
ã
ENTRY
ä
}
1
y
ã
INS
ä
(above
{
)
.9
to change
12
to
11.9
. Press
Í
to evaluate the expression.
11. If the amount above is to be divided among
seven people, how much will each person get?
To divide the last calculated amount by seven,
press
¥
7
, followed by
Í
.
As soon as you press
¥
,
Ans
à
is displayed at
the beginning of the new expression.
Ans
is a
variable that contains the last calculated
answer.
6 Getting Started
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Defining a Function: Box with Lid
Take a 200×250 mm. sheet of paper and cut X-by-X squares from two corners and
X-by-125 mm. rectangles from the other two corners. Now fold the paper into a
box with lid. What X would give the maximum volume V of a box made in this
way? Use tables and graphs to determine the solution.
Begin by defining a function that describes the
v
olume of the box.
From the diagram: 2X + A = W
2X + 2B = L
V = A B X
Substituting: V = (W – 2X) (L
à
2 – X) X
W
X
X
A
BXB
L
1. Press
z
†
Í
to change the
MODE
back
to
Float
.
2. Press
y
ã
Quit
ä
‘
to return to the Home
screen and clear it.
3. Press
200
¿
ƒ
W
y
ã
:
ä
250
¿
ƒ
L
Í
to store the width and length of
the paper.
4. You define functions for tables and graphing on
the
Y=
edit screen. Press
o
to access this
screen.
5. Enter the function for volume as
Y
1
. Press
£
ƒ
W
¹
2
„
¤
£
ƒ
L
¥
2
¹
„
¤
„
Í
to define function
Y
1
in terms of
X
. (
„
lets you enter
X
quickly, without
pressing
ƒ
.)
The
=
sign is highlighted to show that
Y
1
is
selected.
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Defining a Table of Values
The table feature of the TI
.
82 provides numeric information about a function. Use
a table of values from the previously defined function to estimate an answer to
the problem.
1. Press
y
ã
TblSet
ä
(above
p
) to display the
TABLE SETUP
menu.
2. Press
Í
to accept
TblMin=0
.
3. Press
10
Í
to define the table increment
@
Tbl=10
. Leave
Indpnt: Auto
and
Depend: Auto
so the table will be generated automatically.
4. Press
y
ã
TABLE
ä
(above
s
) to display the
table.
Note that the maximum value displayed is at
X=40
. The maximum occurs between
30
and
50
.
5. Press and hold
†
to scroll the table until the
sign change appears. Note that the maximum
length of
X
for this problem occurs where the
sign of
Y
1
(volume) becomes negative.
6. Press
y
ã
TblSet
ä
. Note that
TblMin
has changed
to reflect the first line of the table you last
displayed.
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Zooming In on the Table
You can adjust the way a table is displayed to get more detailed information
about any defined function. By varying the value of
@
Tbl, you can “zoom in” on
the table.
1. Adjust the table setup to get a more accurate
estimate of the maximum size of the cutout.
Press
30
Í
to set
TblMin
. Press
1
Í
to
set
@
Tbl
.
2. Press
y
ã
TABLE
ä
.
3. Use
†
and
}
to scroll the table. Note that the
maximum value displayed is
410256
, which
occurs at
X
=
37
. The maximum occurs between
36 and 38.
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4. Press
y
ã
TblSet
ä
. Press
36
Í
to set
TblMin
.
Press
.1
Í
to set
@
Tbl
.
5. Press
y
ã
TABLE
ä
and use
†
and
}
to scroll the
table.
6. Press
†
and
}
to move the cursor. The
maximum value of
Y
1
at
36.8
is
410264
.
7. Press
~
to display the value of
Y
1
at
36.8
in full
precision,
410264.064
. This would be the
maximum volume of the box if you could cut
your piece of paper at 1 mm. increments.
10 Getting Started
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Changing the Viewing WINDOW
The viewing WINDOW defines the portion of the coordinate plane that appears in
the display. The values of the WINDOW variables determine the size of the
viewing WINDOW. You can view and change these values.
1. Press
p
to display the
WINDOW
variables
edit screen. You can view and edit the values of
the
WINDOW
variables here.
The standard
WINDOW
variables define the
viewing
WINDOW
as shown.
Xmin
,
Xmax
,
Ymin
,
and
Ymax
define the boundaries of the display.
Xscl
and
Yscl
define the distance between tick
marks on the
X
and
Y
axis.
Xmax
Ymin
Ymax
Xscl
Yscl
Xmin
2. Press
†
to move the cursor onto the line to
define
Xmin
. Press
0
Í
.
3. You can enter expressions to define values in
the
WINDOW
editor. Press
200
¥
2
.
4. Press
Í
. The expression is evaluated, and
100
is stored in
Xmax
. Press
10
Í
to set
Xscl
as
10
.
5. Press
0
Í
500000
Í
100000
Í
to
define the
Y
WINDOW
variables.
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Displaying and Tracing the Graph
Now that you have defined the function to be graphed and the WINDOW in which
to graph it, you can display and explore the graph. You can trace along a function
with TRACE.
1. Press
s
to graph the selected function in
the viewing
WINDOW
.
The graph of
Y
1
=(W–2X)(L
à
2–X)X
is shown in
the display.
2. Press
~
once to display the free-moving graph
cursor just to the right of the center of the
screen. The bottom line of the display shows the
X
and
Y
coordinate values for the position of the
graph cursor.
3. Use the cursor-keys (
|
,
~
,
}
, and
†
) to
position the free-moving cursor at the apparent
maximum of the function.
As you move the cursor,
X
and
Y
coordinate
values are updated continually with the cursor
position.
4. Press
r
. The
TRACE
cursor appears on the
Y
1
function near the middle of the screen.
1
in
the upper right corner of the display shows that
the cursor is on
Y
1
. As you press
|
and
~
, you
trace along
Y
1
, one
X
dot at a time, evaluating
Y
1
at each
X
.
Press
|
and
~
until you are on the maximum
Y
value. This is the maximum of
Y
1
(X)
for the
X
pixels. (There may be a maximum “in between”
pixels.)
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Zooming on the Graph
You can magnify the viewing WINDOW around a specific location using the
ZOOM instructions to help identify maximums, minimums, roots, and
intersections of functions.
1. Press
q
to display the
ZOOM
menu.
This menu is typical of TI
.
82 menus. To select
an item, you may either press the number to the
left of the item, or you may press
†
until the
item number is highlighted and then press
Í
.
2. To zoom in, press
2
. The graph is displayed
again. The cursor has changed to indicate that
you are using a
ZOOM
instruction.
3. Use
|
,
}
,
~
, and
†
to position the cursor near
the maximum value on the function and press
Í
.
The new viewing
WINDOW
is displayed. It has
been adjusted in both the
X
and
Y
directions by
factors of 4, the values for
ZOOM
factors.
4. Press
p
to display the new
WINDOW
settings.
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Finding the Calculated Maximum
You can use a CALC operation to calculate a local maximum of a function.
1. Press
y
ã
CALC
ä
to display the
CALCULATE
menu. Press
4
to select
maximum
.
The graph is displayed again, with a prompt for
Lower Bound?
2. Use
|
to trace along the curve to a point to the
left of the maximum and then press
Í
.
A triangle at the top of the screen indicates the
selected bound. A new prompt is displayed for
Upper Bound?
3. Use
~
to trace along the curve to a point to the
right of the maximum and then press
Í
.
A triangle at the top of the screen indicates the
selected bound. A new prompt is displayed for
Guess?
4. Use
|
to trace to a point near the maximum and
press
Í
. The answer is displayed at the
bottom of the display.
Note how the values for the calculated
maximum compared with the maximums found
with the free-moving cursor,
TRACE
, and the
table.
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Other Features
Getting Started introduced you to basic calculator operation and the table and
function graphing features of the TI
.
82. The remainder of this guidebook
describes these features in more detail and also covers other capabilities of the
TI
.
82.
Graphing
You can store, graph, and analyze up to ten functions (Chapter 3), up to six
parametric functions (Chapter 4), and up to six polar functions (Chapter 5).
You can use
DRAW
operations to annotate graphs (Chapter 8).
Sequences
You can generate sequences and graph them over time or as web plots.
(Chapter 6)
Tables
You can create function evaluation tables to analyze multiple functions
simultaneously. (Chapter 7)
Matrices
You can enter and save up to five matrices and perform standard matrix
operations on them. (Chapter 10)
Lists
You can enter and save up to six lists for use in statistical analysis. You also
can use lists to evaluate expressions at multiple values simultaneously and
to graph a family of curves. (Chapter 11)
Statistics
You can perform one-variable and two-variable list-based statistical
analysis, including median-median line and regression analysis, and plot the
data as histograms, points,
x-y
lines, or box-and-whisker plots. You can
define and save three statistical plot definitions. (Chapters 12).
Programming
You can enter and save programs that include extensive control and
input/output instructions. (Chapter 13)
Split Screen
You can show simultaneously the graph screen and a related editor, such as
the
Y=
screen, table, list editor, or Home screen. (Chapter 9)
Operating the TI
.
82 1-1
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Chapter 1: Operating the TI-82
This chapter describes the TI
.
82 and provides general information about its
operation.
Chapter Contents
Turning the TI
.
82 On and Off
......................
1-2
Setting the Display Contrast
.....................
1
-
3
The Display
................................
1
-
4
Entering Expressions and Instructions
.............
1
-
6
TI
.
82 Edit Keys
..............................
1
-
8
Setting Modes
...............................
1
-
9
TI
.
82 Modes
................................
1
-
10
Variable Names
..............................
1
-
12
Storing and Recalling Variable Values
..............
1
-
13
Last Entry
..................................
1
-
14
Last Answer
.................................
1
-
16
TI
.
82 Menus
................................
1
-
17
VARS
and
Y
.
VARS
Menus
.......................
1
-
19
EOS
é
(
Equation Operating System
)
................
1
-
20
Error Conditions
.............................
1
-
22
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.
82
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Turning the TI-82 On and Off
To turn the TI
.
82 on, press the
É
key. To turn it off, press and release
y
and
then press
M
. After about five minutes without any activity, APD
é
(Automatic
Power Down™) turns the TI
.
82 off automatically.
Turning the Calculator On
Press
É
to turn the TI
.
82 on.
¦
If you pressed
y
ã
OFF
ä
to turn the calculator off, the display shows
the Home screen as it was when you last used it, and errors are cleared.
¦
If APD turned the calculator off, the TI
.
82, including the display, cursor,
and any error conditions, will be exactly as you left it.
Turning the Calculator Off
Press and release
y
and then press
ã
OFF
ä
to turn the TI
.
82 off.
¦
Any error condition is cleared.
¦
All settings and memory contents are retained by Constant Memory
é
.
APD™ (Automatic Power Down™)
To prolong the life of the batteries, APD turns the TI
.
82 off automatically
after several minutes without any activity. When you press
É
, the TI
.
82
will be exactly as you left it.
¦
The display, cursor, and any error conditions are exactly as you left
them.
¦
All settings and memory contents are retained by Constant Memory.
Batteries
The TI
.
82 uses four AAA alkaline batteries and has a user-replaceable back-
up lithium battery. To replace batteries without losing any information
stored in memory, follow the directions on page B
.
2.
Operating the TI
.
82 1-3
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Setting the Display Contrast
The brightness and contrast of the display depends on room lighting, battery
freshness, viewing angle, and adjustment of the display contrast. The contrast
setting is retained in memory when the TI
.
82 is turned off.
Adjusting the Display Contrast
You can adjust the display contrast to suit your viewing angle and lighting
conditions at any time. As you change the contrast setting, the display
contrast changes, and a number in the upper right corner indicates the
current contrast setting between 0 (lightest) and 9 (darkest).
Note that there are 32 different contrast levels, so each number 0 through 9
represents more than one setting.
To adjust the contrast:
1. Press and release the
y
key.
2. Use one of two keys:
¦
To increase the contrast, press and hold
}
.
¦
To decrease the contrast, press and hold
†
.
Note: If you adjust the contrast setting to zero, the display may become
completely blank. If this happens, press and release
y
and then press and
hold
}
until the display reappears.
When to Replace Batteries
When the batteries are low, the display begins to dim (especially during
calculations), and you must adjust the contrast to a higher setting. If you
find it necessary to set the contrast to a setting of 8 or 9, you should replace
the four AAA batteries soon.
Note: The display contrast may appear very dark after you change
batteries. Press and release
y
and then press and hold
†
to lighten the
display.
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.
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The Display
The TI
.
82 displays both text and graphics. Graphics are described in Chapter 3.
The TI
.
82 also can display a split screen, showing graphics and text
simultaneously (Chapter 9).
Home Screen
The Home screen is the primary screen of the TI
.
82, where you enter
instructions to be executed and expressions to be evaluated and see the
answers.
Displaying Entries and Answers
When text is displayed, the TI
.
82 screen can have up to eight lines of up to
16 characters per line. If all lines of the display are filled, text “scrolls” off
the top of the display. If an expression on the Home screen, the
Y=
editor
(Chapter 3), or the program editor (Chapter 13) is longer than one line, it
wraps to the beginning of the next line. On numeric editors such as the
WINDOW
screen (Chapter 3), an expression scrolls to the left and right.
When an entry is executed on the Home screen, the answer is displayed on
the right side of the next line.
Entry
Answer
The
MODE
settings control the way expressions are interpreted and
answers are displayed (page 1
.
10).
If an answer, such as a list or matrix, is too long to display in its entirety,
ellipsis marks (...) are shown at the left or right. Use
~
and
|
to scroll the
answer and view all of it.
Entry
Answer
Returning to the Home Screen
To return to the Home screen from any other screen, press
y
ã
QUIT
ä
.
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.
82 1-5
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Display Cursors
In most cases, the appearance of the cursor indicates what will happen
when you press the next key.
Cursor Appearance Meaning
Entry Solid blinking
rectangle
The next keystroke is entered at the
cursor; it types over any character.
INS
(insert) Blinking underline The next keystroke is inserted in front
of the cursor location.
2nd
Blinking
#
(arrow) The next keystroke is a
2nd
operation.
ALPHA
Blinking
A
The next keystroke is an alphabetic
character.
“full” Checkerboard
rectangle
You have entered the maximum
characters in a name, or memory is
full.
If you press
ƒ
or
y
during an insertion, the underline cursor changes
to an underlined
A
or
#
cursor.
If you press
y
or
ƒ
on a screen on which there is no edit cursor
(such as the
MODE
screen or a graph),
#
or
A
appears in the upper right
corner.
Graphs and the screens for viewing and editing tables, matrices, and lists
have different cursors, which are described in the appropriate chapter.
Busy Indicator
When the TI
.
82 is calculating or graphing, a moving vertical bar shows in
the upper right of the display as a busy indicator. (When you pause a graph
or a program, the busy indicator is a dotted bar.)
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.
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Entering Expressions and Instructions
On the TI
.
82, you can enter expressions, which return a value, in most places
where a value is required. You enter instructions, which initiate an action, on the
Home screen or in the program editor (Chapter 13).
Expressions
An expression is a complete sequence of numbers, variables, functions, and
their arguments that evaluate to a single answer. On the TI
.
82, you enter an
expression in the same order that it normally is written. For example,
p
R
2
is an expression.
Expressions can be used on the Home screen to calculate an answer. In
most places where a value is required, expressions may be used to enter a
value.
Entering an Expression
To create an expression, enter numbers, variables, and functions from the
keyboard and menus. An expression is completed when you press
Í
,
regardless of the cursor location. The entire expression is evaluated
according to EOS rules (page 1
.
20), and the answer displayed.
Most TI
.
82 functions and operations are symbols with several characters in
them. You must enter the symbol from the keyboard or menu, not spell it
out. For example, to calculate the log of 45, you must press
«
4 5
. You
cannot type in the letters
L O G
. (If you type
LOG
, the TI
.
82 interprets the
entry as implied multiplication of the variables
L
,
O
, and
G
.)
Calculate 3.76 ÷ (-7.9 +
‡
5) + 2 log 45.
3.76
¥
£
Ì
7.9
Ã
y
ã
‡
ä
5
¤
Ã
2
«
45
Í
Multiple Entries on a Line
To enter more than one expression or instruction on a line, separate them
with a colon (
:
). They are all stored together in
Last Entry
(page 1
.
14).
Operating the TI
.
82 1-7
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Entering a Number in Scientific Notation
1. Type the part of the number that precedes the exponent. This value can
be an expression.
2. Press
y
ã
EE
ä
.
E
appears in the display.
3. If the exponent is negative, press
Ì
and then type the exponent, which
can be one or two digits.
Entering a number in scientific notation does not cause the answers to be
displayed in scientific or engineering notation. The display format is
determined by the
MODE
settings (page 1
.
10) and the size of the number.
Functions
A function returns a value. For example,
÷
,
-
,
+
,
‡
, and
log
were the
functions in the previous example. In general, the names of functions on
the display begin with a lowercase letter. Some functions take more than
one argument, which is indicated by a
(
at the end of the name. For
example,
min(
requires arguments,
min(5,8)
.
Instructions
An instruction initiates an action. For example,
ClrDraw
is an instruction
that clears any drawn elements from a graph. Instructions cannot be used
in expressions. In general, the names of instructions begin with a capital
letter. Some instructions require more than one argument, which is
indicated by a
(
at the end of the name. For example,
Circle(
requires three
arguments,
Circle(0,0,5)
.
Interrupting a Calculation
While the busy indicator is displayed, indicating that a calculation or a
graph is in progress, you can press
É
to stop the calculation. (There may
be a delay.) Except in graphing, the
ERR:BREAK
screen is shown.
¦
To go to where the interruption occurred, select
Goto
.
¦
To return to the Home screen, select
Quit
.
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.
82
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TI-82 Edit Keys
~
or
|
Moves the cursor within an expression. These keys repeat.
}
or
†
Moves the cursor between lines. These keys repeat.
¦
On top line of an expression on the Home screen,
}
moves the
cursor to beginning of expression.
¦
On bottom line of an expression on the Home screen,
†
moves
the cursor to end of expression.
y
|
Moves the cursor to beginning of expression.
y
~
Moves the cursor to end of expression.
Í
Evaluates an expression or executes an instruction.
‘ ¦
On a line with text on the Home screen, clears (blanks) the
current line.
¦
On a blank line on the Home screen, clears everything on the
Home screen.
¦
In an editor, clears (blanks) expression or value where cursor is
located; it does not store a zero.
{
Deletes character at cursor. This key repeats.
y
ã
INS
ä
Inserts characters at underline cursor. To end insertion, press
y
ã
INS
ä
or a cursor-key.
y
Next keystroke performs a
2nd
operation (the blue operation to the
left above a key). The cursor changes to an
#
. To cancel
2nd
, press
y
.
ƒ
Next keystroke is an
ALPHA
character (the gray character to the
right above the key). The cursor changes to an
A
. To cancel
ALPHA
,
press
ƒ
or a cursor-key.
y
ã
A-LOCK
ä
Sets
ALPHA-LOCK
; each subsequent keystroke is an
ALPHA
character. The cursor changes to an
A
. To cancel
ALPHA-LOCK
,
press
ƒ
. Note that prompts for names automatically set the
keyboard in
ALPHA-LOCK
.
„
Allows you to enter an
X
in
Func
MODE
, a
T
in
Par
MODE
, or a
q
in
Pol
MODE
without pressing
ƒ
first.
Operating the TI
.
82 1-9
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Setting Modes
Modes control how numbers and graphs are displayed and interpreted. MODE
settings are retained by Constant Memory
é
when the TI
.
82 is turned off. All
numbers, including elements of matrices and lists, are displayed according to the
current MODE settings.
Checking MODE Settings
Press
z
to display the
MODE
settings. The current settings are
highlighted. The specific
MODE
settings are described on the following
pages.
Normal Sci Eng
Numeric display format
Float 0123456789
Number of decimal places
Radian Degree
Unit of angle measure
Func Par Pol Seq
Type of graphing
Connected Dot
Whether to connect graph points
Sequential Simul
Whether to plot simultaneously
FullScreen Split
Full or split screen
Changing MODE Settings
1. Use
†
or
}
to move the cursor to the line of the setting that you want
to change. The setting that the cursor is on blinks.
2. Use
~
or
|
to move the cursor to the setting that you want.
3. Press
Í
.
Leaving the MODE Screen
To leave the
MODE
screen:
¦
Press the appropriate keys to go to another screen.
¦
Press
y
ã
QUIT
ä
or
‘
to return to the Home screen.
Setting a MODE from a Program
You can set a
MODE
from a program by entering the name of the
MODE
as
an instruction; for example,
Func
or
Float
. From a blank line, select the
name from the interactive
MODE
selection screen in the program editor
(Chapter 13); the name is copied to the cursor location. The format for
fixed decimal setting is
Fix
n
.
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.
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TI-82 Modes
The TI
.
82 has seven MODE settings. Three are related to how numeric entries are
interpreted or displayed and four are related to how graphs appear in the display.
Modes are set on the MODE screen (page 1
.
9).
Normal, Sci, Eng
Notation formats affect only how an answer is displayed on the Home
screen. Numeric answers can display with up to 10 digits and a two-digit
exponent. You can enter a number in any format.
Normal
display format is the way in which we usually express numbers,
with digits to the left and right of the decimal, as in
12346.67
.
Sci
(scientific) notation expresses numbers in two parts. The significant
digits display with one digit to the left of the decimal. The appropriate
power of 10 displays to the right of
E
, as in
1.234667
E
4
.
Eng
(engineering) notation is similar to scientific notation. However, the
number may have one, two, or three digits before the decimal, and the
power-of-10 exponent is a multiple of three, as in
12.34667
E
3
.
Note: If you select normal display format, but the answer cannot display in
10 digits or the absolute value is less than .001, the TI
.
82 changes to
scientific notation for that answer only.
Float, Fix
Decimal settings affect only how an answer is displayed on the Home
screen. They apply to all three notation display formats. You can enter a
number in any format.
Float
(floating) decimal setting displays up to 10 digits, plus the sign and
decimal.
The fixed decimal setting displays the selected number of digits (
0
to
9
) to
the right of the decimal. Place the cursor on the number of decimal digits
you want and press
Í
.
Operating the TI
.
82 1-11
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02/09/01 12:35 PM Page 11 of 22
Radian, Degree
Angle settings control how the TI
.
82 interprets angle values in trig
functions and polar/rectangular conversions.
Radian
interprets the values as radians. Answers display in radians.
Degree
interprets the values as degrees. Answers display in degrees.
Func, Par, Pol, Seq
Func
(function) graphing plots functions where
Y
is a function of
X
(Chapter 3).
Par
(parametric) graphing plots relations where
X
and
Y
are functions of
T
(Chapter 4).
Pol
(polar) graphing plots functions where
R
is a function of
q
(Chapter 5).
Seq
(sequence) graphing plots sequences (Chapter 6).
Connected, Dot
Connected
draws a line between the points calculated for the selected
functions.
Dot
plots only the calculated points of the selected functions.
Sequential, Simul
Sequential
graphing evaluates and plots one function completely before the
next function is evaluated and plotted.
Simul
(simultaneous) graphing evaluates and plots all selected functions
for a single value of
X
and then evaluates and plots them for the next value
of
X
.
FullScreen, Split
FullScreen
uses the entire screen to display a graph or edit screen.
Split
screen displays the current graph on the upper portion of the screen
and the Home screen or an editor on the lower portion (Chapter 9).
1-12 Operating the TI
.
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02/09/01 12:35 PM Page 12 of 22
Variable Names
On the TI
.
82 you can enter and use several types of data, including real numbers,
matrices, lists, functions, stat plots, graph databases, and graph pictures.
Variables and Defined Items
The TI
.
82 uses preassigned names for variables and other items saved in
memory.
Variable type Names
Real numbers
A
,
B
, . . . ,
Z
,
q
Matrices
ã
A
ä
,
ã
B
ä
,
ã
C
ä
,
ã
D
ä
,
ã
E
ä
Lists
L
1
,
L
2
,
L
3
,
L
4
,
L
5
,
L
6
Functions
Y
1
,
Y
2
, . . . ,
Y
9
,
Y
0
Parametric equations
X
1T
/Y
1T
, . . . ,
X
6T
/Y
6T
Polar functions
r
1
,
r
2
,
r
3
,
r
4
,
r
5
,
r
6
Sequence functions
U
n
,
V
n
Stat plots
Plot1
,
Plot2
,
Plot3
Graph databases
GDB1
,
GDB2
, . . . ,
GDB6
Graph pictures
Pic1
,
Pic2
, . . . ,
Pic6
System variables
Xmin
,
Xmax
, and others
Programs have user-defined names also and share memory with variables.
Programs are entered and edited from the program editor (Chapter 13).
You can store to matrices (Chapter 10), lists (Chapter 11), system variables
such as
Xmax
(Chapter 3) or
TblMin
(Chapter 7), and all functions
(Chapters 3, 4, 5, and 6) from the Home screen or from a program. You can
store to matrices (Chapter 10), lists (Chapter 12), and functions (Chapter 3)
from editors. You can store to a matrix element (Chapter 10) or a list
element (Chapter 11). Graph databases and pictures are stored and recalled
using instructions from the
DRAW
menu (Chapter 8).
Operating the TI
.
82 1-13
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 13 of 22
Storing and Recalling Variable Values
Values are stored to and recalled from memory using variable names. When an
expression containing the name of a variable is evaluated, the value of the
variable at that time is used.
Storing Values in a Variable
You can store a value to a variable from the Home screen or a program
using the
¿
key. Begin on a blank line.
1. Enter the value that you want to store (which can be an expression).
2. Press
¿
. The symbol
!
is copied to the cursor location.
3. Press
ƒ
, then the letter of the variable to which you want to store
the value.
4. Press
Í
. If you entered an expression, it is evaluated. The value is
stored in the variable.
Displaying a Variable Value
To display the value of a variable, enter the name on a blank line on the
Home screen, and press
Í
.
RCL (Recall)
You can copy variable contents to the current cursor location. Press
y
ã
RCL
ä
, and then enter the name of the variable in one of the following ways:
¦
Press
ƒ
and then the letter of the variable.
¦
Press
y
and the name of the list.
¦
Press
and select the name of the matrix.
¦
Press
y
ã
Y
.
VARS
ä
and select the type and name of the function.
¦
Press
and select the name of the program (in the program editor
only).
You can edit the characters copied to the expression without affecting the
value in memory.
Note: When an error (such as a variable with no assigned value) occurs on
the
RCL
line, the name is cleared automatically for you to enter the correct
name. To leave
RCL
without recalling a value, press
‘
.
1-14 Operating the TI
.
82
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 14 of 22
Last Entry
When you press
Í
on the Home screen to evaluate an expression or execute
an instruction, the expression or instruction is stored in a storage area called
Last Entry, which you can recall. When you turn the TI
.
82 off, Last Entry is
retained in memory.
Using Last Entry
You can recall
Last Entry
and edit it from the Home screen or any editor.
Press
y
ã
ENTRY
ä
. On the Home screen or a numeric editor, the current
line is cleared and the
Last Entry
is copied to the line. The cursor is
positioned at the end of the entry. In the program editor, the
Last Entry
is
inserted at the cursor location. Because the TI
.
82 updates the
Last Entry
storage area only when
Í
is pressed, you can recall the previous entry
even if you have begun entering the next expression. However, when you
recall
Last Entry
, it replaces what you have typed.
5
Ã
7
Í
y
ã
ENTRY
ä
Multiple Entries on a Line
To enter more than one expression or instruction on a line, separate them
with a colon (
:
). They are all stored together in
Last Entry
(page 1
.
14).
If the previous entry contained more than one expression or instruction,
separated with a colon (page 1
.
7), they all are recalled. You can recall all
entries on a line, edit any of them, and then execute all of them.
Using the equation A=
p
r
2
, use trial and error to find the radius of a circle
that covers 200 square centimeters. Use 8 as your first guess.
8
¿
ƒ
R
y
ã
:
ä
y
ãpä
ƒ
R
¡
Í
y
ã
ENTRY
ä
y
|
7
y
ã
INS
ä
.95
Í
Continue until the answer is as accurate as you want.
Operating the TI
.
82 1-15
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 15 of 22
Reexecuting the Previous Entry
To execute
Last Entry
press
Í
on a blank line on the Home screen; the
entry does not display again.
0
¿
ƒ
N
Í
ƒ
N
Ã
1
¿
ƒ
N
y
ã
:
ä
ƒ
N
¡
Í
Í
Í
Accessing a Previous Entry
The TI
.
82 retains as many of the previous entries as is possible (up to a
total of 128 bytes) in the
Last Entry
storage area. You can access those
entries by continuing to press
y
ã
ENTRY
ä
. (If a single entry is more than
128 bytes, it is retained for
Last Entry
, but it cannot be placed in the
Last Entry
storage area.)
1
¿
ƒ
A
Í
2
¿
ƒ
B
Í
3
¿
ƒ
C
Í
y
ã
ENTRY
ä
Each time you press
y
ã
ENTRY
ä
, the current line is overwritten. If you
press
y
ã
ENTRY
ä
after displaying the oldest item, the newest item is
displayed.
y
ã
ENTRY
ä
1-16 Operating the TI
.
82
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 16 of 22
Last Answer
When an expression is evaluated successfully from the Home screen or from a
program, the TI
.
82 stores the answer to a variable, Ans (Last Answer). Ans may
be a real number, a list, or a matrix. When you turn the TI
.
82 off, the value in Ans
is retained in memory.
Using Ans in an Expression
You can use the variable
Ans
to represent the last answer in most places.
Press
y
ã
ANS
ä
and the variable name
Ans
is copied to the cursor location.
When the expression is evaluated, the TI
.
82 uses the value of
Ans
in the
calculation.
Calculate the area of a garden plot 1.7 meters by 4.2 meters. Then calculate
the yield per square meter if the plot produces a total of 147 tomatoes.
1.7
¯
4.2
Í
147
¥
y
ã
ANS
ä
Í
Continuing an Expression
You can use the value in
Ans
as the first entry in the next expression
without entering the value again or pressing
y
ã
ANS
ä
. On the blank line on
the Home screen, enter the function. The TI
.
82 “types” the variable name
Ans
followed by the function.
5
¥
2
Í
¯
9.9
Í
Storing Answers
To store an answer, store
Ans
to a variable before you evaluate another
expression.
Calculate the area of a circle of radius 5 meters. Then calculate the volume
of a cylinder of radius 5 meters and height 3.3 meters and store in the
variable
V
.
y
ãpä
5
¡
Í
¯
3.3
Í
¿
ƒ
V
Í
Operating the TI
.
82 1-17
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 17 of 22
TI-82 Menus
To leave the keyboard uncluttered, the TI
.
82 uses full-screen menus to access
many operations. The use of specific menus is described in the appropriate
chapters.
Moving from One Menu to Another
A menu key may access more than one menu. The names of the menus
appear on the top line. The current menu is highlighted and the items in
that menu are displayed.
Use
~
or
|
to move the cursor to a different menu.
Selecting an Item from a Menu
The number of the current item is highlighted. If there are more than seven
items on the menu, a
$
appears on the last line in place of the
:
(colon).
Menu items that end in
...
(ellipsis marks) access another menu.
There are two methods of selecting from a menu.
¦
Press the number of the item you want to select.
¦
Use
†
and
}
to move the cursor to the item you want to select and
then press
Í
.
Leaving a Menu without Making a Selection
After you make a selection from a menu, you usually are returned to the
screen where you were.
To leave a menu without making a selection, do any of the following:
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
¦
Press
‘
to return to the screen where you were.
¦
Display a different menu by pressing the appropriate key, such as
.
¦
Select another screen by pressing the appropriate key, such as
p
.
1-18 Operating the TI
.
82
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 18 of 22
Calculate 6
3
‡
27.
1. Press
6
. Press
to display the
MATH
menu.
2. To select
3
‡
, you may either press
4
or press
†
†
†
Í
.
3. Press
27
and then press
Í
to evaluate the expression.
Operating the TI
.
82 1-19
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 19 of 22
VARS and Y-VARS Menus
Occasionally you may want to access the names of functions and system
variables to use in an expression or to store to them directly. Use the VARS or
Y
.
VARS menus to access the names of variables such as Xmin and functions
such Y
1
.
VARS Menu
The
VARS
menu accesses the names of
WINDOW
variables such as
Xmin
and
Tstep
, the user-defined
ZOOM
variables such as
ZXmin
, graph
databases and graph pictures such as
GDB1
and
Pic2
, statistics variables
such as
v
,
RegEQ
and
Q
1
, and table variables such as
TblMin
.
Press
to display the
VARS
menu. Some of the items access more than
one menu of variable names.
VARS
1: Window
…
Names of
X/Y
,
T/
q
,
U/V
variables
2: Zoom
…
Names of
ZX/ZY
,
ZT/Z
q
,
ZU
variables
3: GDB
…
Names of
GDB
n
variables
4: Picture
…
Names of
Pic
n
variables
5: Statistics
…
X/Y
,
G
,
EQ
,
BOX
,
PTS
variables
6: Table
…
Names of
Table
variables
Y-VARS Menu
The
Y-VARS
menu accesses the names of functions and the instructions to
select or deselect functions from a program or the Home screen.
Press
y
ã
Y-VARS
ä
to display the
Y-VARS
menu.
Y-VARS
1: Function
…
Displays names of
Y
n
functions
2: Parametric
…
Displays names of
X
n
T
,
Y
n
T
functions
3: Polar
…
Displays names of
r
n
functions
4: Sequence
…
Displays names of
U
n
,
V
n
functions
5: On/Off
…
Lets you select/deselect functions
Accessing a Name from a VARS or Y-VARS Menu
1. Press
or
y
ã
Y-VARS
ä
. The
VARS
or
Y-VARS
menu is displayed.
2. Select the type of name you want;
Picture...
or
Polar...
, for example.
¦
In
VARS
, use
~
or
|
to move to the menu you want, if necessary.
¦
In
Y-VARS
, a single menu is displayed.
3. Select the name you want from the menu. It is copied to the cursor
location.
1-20 Operating the TI
.
82
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 20 of 22
EOS™ (Equation Operating System)
The Equation Operating System (EOS
é
) defines the order in which functions in
expressions are entered and evaluated on the TI
.
82. EOS lets you enter numbers
and functions in a simple, straightforward sequence.
Order of Evaluation
A function returns a value. EOS evaluates the functions in an expression in
the following order:
1
Functions that are entered after the argument, such as
2
,
-1
,
!
,
¡
,
r
,
T
, and conversions.
2
Powers and roots, such as
2^5
or
5
x
‡
32
.
3
Implied multiplication where the second argument is a number,
v
ariable name, list, or matrix or begins with an open parenthesis,
such as
4A
,
3
ã
B
ä
,
(A+B)4
, or
4(A+B)
.
4
Single-argument functions that precede the argument, such as
negation,
‡
,
sin
, or
log
.
5
Implied multiplication where the second argument is a
multiargument function or a single-argument function that
precedes the argument, such as
2nDeriv(A
2
,A,6)
or
Asin 2
.
6
Permutations (
nPr
) and combinations (
nCr
).
7
Multiplication and division.
8
Addition and subtraction.
9
Relational functions, such as
>
or
.
10
Logic operator
and
.
11
Logic operators
or
and
xor
.
Within a priority group, EOS evaluates functions from left to right.
However, two or more single-argument functions that precede the same
argument are evaluated from right to left. For example,
sin fPart ln 8
is
evaluated as
sin(fPart(ln 8))
.
Calculations within a pair of parentheses are evaluated first. Multiargument
functions, such as
nDeriv(A
2
,A,6)
, are evaluated as they are encountered.
Operating the TI
.
82 1-21
8201OPER.DOC TI-82, Chapter 1, English Bob Fedorisko Revised: 02/09/01 12:18 PM Printed:
02/09/01 12:35 PM Page 21 of 22
Implied Multiplication
The TI
.
82 recognizes implied multiplication. For example, it understands
2
p
,
4 sin 46
,
5(1+2)
, and
(2
…
5)7
as implied multiplication.
Parentheses
All calculations inside a pair of parentheses are completed first. For
example, in the expression
4(1+2)
, EOS first evaluates the portion inside
the parentheses,
1+2
, and then multiplies the answer,
3
, by
4
.
You can omit any right (close) parenthesis at the end of an expression. All
“open” parenthetical elements are closed automatically at the end of an
expression and preceding the
!
(store) or display conversion instructions.
Note: If the name of a list or matrix is followed by an open parenthesis, it
does not indicate implied multiplication. It is used to access specific
elements in the list (Chapter 11) or matrix (Chapter 10).
Negation
To enter a negative number, use the negation function. Press
Ì
and then
enter the number. On the TI
.
82, negation is in the fourth group in the EOS
hierarchy. Functions in the first group, such as squaring, are evaluated
before negation.
For example,
M
X
2
is a negative number (or 0);
M
9
2
is
M
81
. Use parentheses to
square a negative number:
(
M
9)
2
.
Note: Use the
¹
key for subtraction and the
Ì
key for negation. If you
press
¹
to enter a negative number, as in
9
¯
¹
7
, or if you press
Ì
to
indicate subtraction, as in
9
Ì
7
, it is an error. If you press
ƒ
A
Ì
ƒ
B
, it is interpreted as implied multiplication (
A
…M
B
).
1-22 Operating the TI
.
82
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02/09/01 12:35 PM Page 22 of 22
Error Conditions
The TI
.
82 detects any errors at the time it evaluates an expression, executes an
instruction, plots a graph, or stores a value. Calculations stop and an error
message with a menu displays immediately. Error codes and conditions are
described in detail in Appendix B.
Diagnosing an Error
If the TI
.
82 detects an error, it displays the error screen.
The top line indicates the general type of error, such as
SYNTAX
or
DOMAIN
. Additional information about each error message is in Appendix
B.
¦
If you select
Goto
, the cursor is displayed at the location where the
error was detected.
Note: If a syntax error was detected in the contents of a
Y=
function
during program execution, this option returns the user to the
Y=
editor,
not the program.
¦
If you select
Quit
or press
y
ã
QUIT
ä
or
‘
, you return to the Home
screen.
Correcting an Error
1. Note the type of the error.
2. Select
Goto
, if that option is available, and look at the expression for
syntax errors, especially at and in front of the cursor location.
3. If the error in the expression is not readily apparent, turn to Appendix B
and read the information about the error message.
4. Correct the expression.
Math, Angle, and Test Operations 2-1
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 1 of 16
Chapter 2: Math, Angle, and Test Operations
This chapter describes math, angle, and relational operations that are available
on the TI
.
82. The most commonly used functions are accessed from the
keyboard; others are accessed through full-screen menus.
Chapter Contents
Getting Started: Lottery Chances
...................
2-2
Keyboard Math Operations
.......................
2-3
MATH MATH
Operations
.........................
2-5
MATH NUM
(Number) Operations
..................
2-9
MATH HYP
(Hyperbolic) Operations
.................
2-11
MATH PRB
(Probability) Operations
.................
2-12
ANGLE
Operations
.............................
2-13
TEST TEST
(Relational) Operations
.................
2-15
TEST LOGIC
(Boolean) Operations
.................
2-16
2-2 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 2 of 16
Getting Started: Lottery Chances
Getting Started is a fast-paced introduction. Read the chapter for details.
Suppose you want to enter a lottery where 6 numbers will be drawn out of 49. To
win, you must pick all 6 numbers (in any order). What is the probability of winning
if you buy one ticket? What is the probability of winning if you buy five tickets?
1. Determine the number of combinations possible.
On the Home screen, press
49
to enter the total
number of items. Press
|
to display the
MATH PRB
menu. Press
3
or
†
†
Í
to select
nCr
. Press
6
to enter the number of items
selected.
2. Press
Í
to evaluate the expression. This is
the total number of possible combinations of 6
numbers drawn from a set of 49 numbers. With
one ticket, you have one chance in 13,983,816 of
winning.
3. To calculate the probability of winning with one
ticket, press
1
¥
y
ã
ANS
ä
Í
. The answer is
expressed in scientific notation on the TI
.
82
because it is so small. The decimal equivalent is
0.00000007151123842.
4. To calculate the probability of winning with five
tickets, press
¯
5
Í
. Again, the answer is too
small to display in fixed notation. The decimal
equivalent is 0.0000003575561921.
Math, Angle, and Test Operations 2-3
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 3 of 16
Keyboard Math Operations
The most commonly used math functions are on the keyboard.
Using Lists with Functions
Functions that are valid for lists return a list calculated on an element-by-
element basis. If two lists are used in the same expression, they must be
the same length.
+ (Add), – (Subtract),
…
(Multiply),
à
(Divide)
+
(addition
Ã
),
–
(subtraction
¹
),
…
(multiplication
¯
), and
à
(division
¥
)
may be used with numbers, expressions, lists, or matrices (Chapter 10).
valueA
+
valueB
,
valueA
–
valueB
,
valueA
…
valueB
,
valueA
à
valueB
Trig Functions
The trigonometric functions may be used with numbers, expressions, or
lists. They are interpreted according to the current
Radian
/
Degree
MODE
setting. For example,
sin 30
in
Radian
MODE
returns
M
.9880316241
; in
Degree
MODE
it returns
.5
.
sin
value
,
cos
value
,
tan
value
sin
.
1
,
cos
.
1
, and
tan
.
1
are the inverse trig functions (arcsine, arccosine, and
arctangent).
sin
.
1
value
,
cos
.
1
value
,
tan
.
1
value
^
(Power),
2
(Square),
‡
(Square Root)
^
(power
›
),
2
(squared
¡
), and
‡
(square root
y
ã
‡
ä
) may be used with
numbers, expressions, lists, or matrices (Chapter 10).
value
^
power
,
value
2
,
‡
value
Note: Raising a negative number to a noninteger power can result in a
complex number, which returns an error.
.
1
(Inverse)
.
1
(inverse
—
) may be used with numbers, expressions, lists, or matrices
(Chapter 10).The multiplicative inverse is the equivalent of the reciprocal,
1
à
x.
value
.
1
2-4 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 4 of 16
log, 10^, ln
log
(logarithm
«
),
10^
(power of ten
y
ã
10
x
ä
), and
ln
(natural log
y
ã
ln
ä
) may be used with a number, expression, or list.
log
value
,
10^
power
,
ln
value
e^
e^
(exponential
y
ã
e
x
ä
) may be used with a number, expression, or list.
e^
returns the constant e raised to a power.
e^1
returns the value of the
constant e.
e^
power
M
(Negation)
M
(negation
Ì
) returns the negative of a number, expression, list, or matrix
(Chapter 10). The narrow negation symbol (
M
) distinguishes negation from
the subtraction or minus
¹
(
N
).
M
value
EOS rules (Chapter 1) determine when negation is evaluated. For example,
M
A
2
returns a negative number (squaring is evaluated before negation
according to EOS rules). Use parentheses to square a negated number,
(
M
A)
2
.
abs
abs
(absolute value) returns the absolute value of a number, expression,
list, or matrix (Chapter 10).
abs
value
p
(Pi)
Pi is stored as a constant in the TI
.
82. Press
y
ã
p
ä
to copy the symbol
p
to
the cursor location. The number 3.1415926535898 is used internally in
calculations.
Math, Angle, and Test Operations 2-5
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 5 of 16
MATH MATH Operations
To display the MATH MATH menu, press
. When you select an item from the
menu, the name is copied to the cursor location. Functions that are valid for lists
return a list calculated on an element-by-element basis.
MATH MATH Menu
MATH NUM HYP PRB
1:
8
Frac
Display answer as fraction
2:
8
Dec
Display answer as decimal
3:
3
Cube
4:
3
‡
Cube root
5:
x
‡
n
th
root
6: fMin(
Minimum of a function
7: fMax(
Maximum of a function
8: nDeriv(
Numerical derivative
9: fnInt(
Function integral
0: solve(
Solution (root) of a function
8
Frac
8
Frac
(display as fraction) displays an answer as the rational equivalent.
The answer may be a number, expression, list, or matrix. If it cannot be
simplified or the denominator is more than three digits, the decimal
equivalent is returned.
8
Frac
is valid only at the end of an expression.
expression
8
Frac
8
Dec
8
Dec
(display as decimal) displays an answer in decimal form.
8
Dec
is
valid only at the end of an expression.
expression
8
Dec
2-6 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 6 of 16
3
(Cube)
3
(cube,
MATH MATH
item
3
) returns the cube of a number, expression, list,
or square matrix (Chapter 10).
value
3
3
‡
(Cube Root)
3
‡
(cube root,
MATH MATH
item
4
) returns the cube root of a number,
expression, or list.
3
‡
value
x
‡
(Root)
x
‡
(root,
MATH MATH
item
5
) returns the
n
th
real root of a number,
expression, or list.
n
th
root
x
‡
value
fMin(, fMax(
fMin(
(function minimum,
MATH MATH
item
6
) and
fMax(
(function
maximum,
MATH MATH
item
7
) return the value at which the minimum or
maximum value of
expression
with respect to
variable
occurs, between
lower
and
upper
values for
variable
.
lower
must be less than
upper
.
fMin(
and
fMax(
are not valid in
expression
. The accuracy is controlled by
tolerance
(optional; if not specified, 1
E
.
5 is used). If there is no finite
minimum or maximum in the interval, usually (depending on
expression
)
an error occurs.
fMin(
expression
,
variable
,
lower
,
upper
)
or
fMin(
expression
,
variable
,
lower
,
upper
,
tolerance
)
Math, Angle, and Test Operations 2-7
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 7 of 16
nDeriv(
nDeriv(
(numerical derivative,
MATH MATH
item
8
) returns an approximate
derivative of
expression
with respect to
variable
, given the
value
at which
to calculate the derivative, and
H
(optional; if none is specified, 1
E
.
3 is
used).
nDeriv(
expression
,
variable
,
value
)
or
nDeriv(
expression
,
variable
,
value
,
H
)
nDeriv(
uses the symmetric difference quotient method, which
approximates the numerical derivative value as the slope of the secant line
through the points:
(
value
–
H
,
expression
(
value
–
H
)) and
(
value
+
H
,
expression
(
value
+
H
))
As
H
gets smaller, the approximation usually gets more accurate.
nDeriv(
can be used once in
expression
. Because of the method,
nDeriv(
can return a false derivative value at a nondifferentiable point.
fnInt(
fnInt(
(function integral,
MATH MATH
item
9
) returns the numerical integral
(Gauss-Kronrod method) of
expression
with respect to
variable
, given
lower
limit,
upper
limit, and a
tolerance
(optional; if none is specified, 1
E
.
5
is used).
fnInt(
expression
,
variable
,
lower
,
upper
)
or
fnInt(
expression
,
variable
,
lower
,
upper
,
tolerance
)
fnInt(
is not valid in
expression
.
2-8 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 8 of 16
solve(
solve(
(
MATH MATH
item
0
) returns a solution (root) of
expression
for
variable
, given an initial
guess
, a
lower
bound, and an
upper
bound within
which a solution is sought (optional, if not specified,
lower
=
.
1
E
99 and
upper
=1
E
99).
solve(
expression
,
variable
,
guess
)
or
solve(
expression
,
variable
,
guess
,{
lower
,
upper
})
expression
is assumed equal to zero. The value of
variable
in memory will
not be updated.
guess
may be a value or a list of two values. Values must be
stored to every variable in
expression
, except
variable
, before
expression
is evaluated.
lower
and
upper
are entered in list format.
Controlling the Solution for solve(
The TI
.
82 solves equations through an iterative process. To control that
process, you should provide a close bound of the solution and at least one
initial guess (which must be within the bounds). This will help to:
¦
Find a solution.
¦
Define which solution you want for equations with multiple solutions.
¦
Find the solution more quickly.
Math, Angle, and Test Operations 2-9
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 9 of 16
MATH NUM (Number) Operations
To display the MATH NUM menu, press
~
. When you select an item from the
menu, the name is copied to the cursor location. Functions that are valid for lists
return a list calculated on an element-by-element basis.
MATH NUM Menu
MATH NUM HYP PRB
1: round(
Round
2: iPart
Integer part
3: fPart
Fractional part
4: int
Greatest integer
5: min(
Minimum value
6: max(
Maximum value
round(
round(
returns a number, expression, list, or matrix rounded to
#decimals
(
9). If
#decimals
is omitted,
value
is rounded to 10 digits.
round(
value
,
#decimals
)
round(
value
)
iPart
iPart
(integer part) returns the integer part or parts of a number,
expression, list, or matrix (Chapter 10).
iPart
value
fPart
fPart
(fractional part) returns the fractional part or parts of a number,
expression, list, or matrix (Chapter 10).
fPart
value
2-10 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 10 of 16
int
int
(greatest integer) returns the largest integer less than or equal to a
number, expression, list, or matrix. The value is the same as
iPart
for
nonnegative numbers and negative integers, but one integer less than
iPart
for negative noninteger numbers.
int
value
min(, max(
min(
(minimum value) returns the smaller of
valueA
or
valueB
or the
smallest element in a list. If two lists are compared, it returns a list of the
smaller of each pair of elements.
max(
(maximum value) returns the larger of
valueA
or
valueB
or the largest
element in a list. If two lists are compared, it returns a list of the larger of
each pair of elements.
min(
valueA
,
valueB
)
or
max(
valueA
,
valueB
)
min(
list
)
or
max(
list
)
min(
listA
,
listB
)
or
max(
listA
,
listB
)
Note: The
min(
and
max(
functions on the
MATH NUM
menu are the same
as the
min(
and
max(
functions on the
LIST MATH
menu.
Math, Angle, and Test Operations 2-11
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 11 of 16
MATH HYP (Hyperbolic) Operations
To display the MATH HYP menu, press
~
~
. When you select an item from
the menu, the name is copied to the cursor location. Functions that are valid for
lists return a list calculated on an element-by-element basis.
MATH HYP Menu
MATH NUM HYP PRB
1: sinh
Hyperbolic sine
2: cosh
Hyperbolic cosine
3: tanh
Hyperbolic tangent
4: sinh
–1
Hyperbolic arcsine
5: cosh
–1
Hyperbolic arccosine
6: tanh
–1
Hyperbolic arctangent
sinh, cosh, tanh
sinh
,
cosh
, and
tanh
are the hyperbolic functions. They are valid for lists.
sinh
value
sinh
–1
, cosh
–1
, tanh
–1
sinh
–1
,
cosh
–1
, and
tanh
–1
are the hyperbolic arcsine, hyperbolic arccosine,
and hyperbolic arctangent functions, respectively. They are valid for lists.
sinh
–1
value
2-12 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 12 of 16
MATH PRB (Probability) Operations
To display the MATH PRB menu, press
|
. When you select an item from the
menu, the name is copied to the cursor location. Functions that are valid for lists
return a list calculated on an element-by-element basis.
MATH PRB Menu
MATH NUM HYP PRB
1: rand
Random number generator
2: nPr
Number of permutations
3: nCr
Number of combinations
4: !
Factorial
rand
rand
(random number) generates and returns a random number greater
than 0 and less than 1. A random number is generated from a seed value. To
control a random number sequence, first store an integer seed value in
rand
. If you store
0
to
rand
, the TI
.
82 uses the factory-set seed value. When
you reset the TI
.
82,
rand
is set to the factory seed.
nPr
nPr
(number of permutations) returns the number of permutations of
items
taken
number
at a time.
items
and
number
must be nonnegative integers.
items
nPr
number
nCr
nCr
(number of combinations) returns the number of combinations of
items
taken
number
at a time.
items
and
number
must be nonnegative
integers.
items
nCr
number
! (Factorial)
!
(factorial) returns the factorial of a positive integer between 0 and 69.
value
!
Math, Angle, and Test Operations 2-13
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 13 of 16
ANGLE Operations
To display the ANGLE menu, press
y
;
. The ANGLE menu displays angle
indicators and instructions. When you select an item from the menu, the name is
copied to the cursor location. Angle entries are interpreted according to the
Radian/Degree MODE setting.
ANGLE Menu
ANGLE
1:
¡
Degree function
2: '
DMS entry notation
3:
r
Radian function
4:
8
DMS
Display as degree/minute/second
5: R
8
Pr(
Returns
R
, given
X
and
Y
6: R
8
P
q
(
Returns
q
, given
X
and
Y
7: P
8
Rx(
Returns
X
, given
R
and
q
8: P
8
Ry(
Returns
Y
, given
R
and
q
Note: Do not enter DMS numbers as
54
¡
32'30"
on the TI
.
82.
54
¡
32'
is
interpreted as implied multiplication of 54
¡
and 32
'
, and
"
is a quote mark
used to enter text.
¡
(Degree)
¡
(degree) lets you designate
angle
as degree, regardless of the current angle
MODE
setting.
angle
may be a list.
angle
¡
' (DMS Entry Notation)
'
(DMS entry notation) lets you enter degrees, minutes, and seconds in DMS
format.
degrees
'
minutes
'
seconds
'
For example, enter
30'1'23'
for 30 degrees, 1 minute, 23 seconds. Note that
the
MODE
setting must be
Degree
(or you must use the
Degree
function)
for the TI
.
82 to interpret the argument as degrees, minutes, and seconds.
Degree
MODE
Radian
MODE
r
(Radians)
r
(radian) lets you designate
angle
as radian, regardless of the current angle
MODE
setting.
angle
may be a list.
angle
r
2-14 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 14 of 16
8
DMS
8
DMS
(display as degree/minute/second) displays
answer
in degree,
minute, second format. The
MODE
setting must be
Degree
for the TI
.
82 to
interpret
answer
as degrees, minutes, and seconds.
8
DMS
is valid only at
the end of a line.
answer
8
DMS
R
8
Pr(, R
8
P
q
(, P
8
Rx(, P
8
Ry(
R
8
Pr(
converts rectangular to polar and returns
R
, and
R
8
P
q
(
converts
rectangular to polar and returns
q
, given
X
and
Y
rectangular coordinate
values.
R
8
Pr(
X
,
Y
)
R
8
P
q
(
X
,
Y
)
P
8
Rx(
converts polar to rectangular and returns
X
, and
P
8
Ry(
converts
polar to rectangular and returns
Y
, given
R
and
q
polar coordinate values.
P
8
Rx(
R
,
q
)
P
8
Ry(
R
,
q
)
Math, Angle, and Test Operations 2-15
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 15 of 16
TEST TEST (Relational) Operations
To display the TEST TEST menu, press
y
:
. When you select from the menu,
the name is copied to the cursor location. These functions are valid for lists; they
return a list calculated on an element-by-element basis.
TEST TEST Menu
TEST LOGIC
True if:
1: =
Equal
2:
ƒ
Not equal to
3: >
Greater than
4:
‚
Greater than or equal to
5: <
Less than
6:
Less than or equal to
=,
ƒ
, >,
‚
, <,
Relational operators compare
valueA
and
valueB
and return
1
if the test is
true or
0
if the test is false.
valueA
and
valueB
can be numbers,
expressions, lists, or matrices (Chapter 10), but they must match in type
and dimension. Relational operators are often used in programs to control
program flow and in graphing to control the graph of a function over
specific values.
valueA
=
valueB
Using Tests
Relational operators are evaluated after mathematical functions according
to EOS rules (Chapter 1).
¦
The expression
2+2=2+3
returns
0
. The TI
.
82 does the addition first
because of EOS rules, and then it compares 4 to 5.
¦
The expression
2+(2=2)+3
returns
6
. The TI
.
82 first performs the
relational test because it is in parentheses, and then it adds 2, 1, and 3.
2-16 Math, Angle, and Test Operations
8202MATH.DOC TI-82, Chapter 2, English Bob Fedorisko Revised: 02/09/01 12:20 PM Printed:
02/09/01 12:36 PM Page 16 of 16
TEST LOGIC (Boolean) Operations
To display the TEST LOGIC menu, press
y
:
~
. When you select from the
menu, the name is copied to the cursor location.
TEST LOGIC Menu
TEST LOGIC
True if:
1: and
Both values are nonzero (true)
2: or
At least one value is nonzero (true)
3: xor
Only one value is zero (false)
4: not
The value is zero (true)
Boolean Operators
Boolean operators are often used in programs to control program flow and
in graphing to control the graph of a function over specific values. Values
are interpreted as zero (false) or nonzero (true).
and, or, xor
and
,
or
, and
xor
(exclusive or) return a value of
1
if a expression is true or
0
if the expression is false, according to the table below.
valueA
and
valueB
can be expressions.
valueA
and
valueB
valueA
or
valueB
valueA
xor
valueB
valueA
valueB
and or xor
ƒ
0
ƒ
0 returns 1 1 0
ƒ
0 0 returns 0 1 1
0
ƒ
0 returns 0 1 1
0 0 returns 0 0 0
not
not
returns 1 if
value
(which can be an expression) is 0.
not
value
Using Boolean Operations
Boolean logic is often used with relational tests. In a program, the following
instructions store
4
into
C
:
Function Graphing 3-1
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 1 of 24
Chapter 3: Function Graphing
This chapter describes function graphing on the TI
.
82 in detail. It also lays the
foundation for using the other graphing features of the TI
.
82.
Chapter Contents
Getting Started: Graphing a Circle
..................
3-2
Defining a Graph
...............................
3-3
Setting Graph Modes
............................
3-4
Defining Functions in the
Y=
List
...................
3-5
Selecting Functions
.............................
3-7
Defining the Viewing
WINDOW
....................
3-8
Setting
WINDOW FORMAT
........................
3-10
Displaying a Graph
.............................
3-11
Exploring a Graph with the Free-Moving Cursor
........
3-13
Exploring a Graph with
TRACE
....................
3-14
Exploring a Graph with
ZOOM
.....................
3-16
Using
ZOOM MEMORY
..........................
3-19
Setting
ZOOM FACTORS
.........................
3-20
Using
CALC
(Calculate) Operations
.................
3-21
3-2 Function Graphing
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 2 of 24
Getting Started: Graphing a Circle
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph a circle of radius 10, centered on the origin in the standard viewing
window. To graph a circle, you must enter separate formulas for the upper and
lower portions of the circle. Then use ZOOM Square to adjust the display to make
the functions appear as a circle.
1. In
Func
MODE
, press
o
to display the
Y=
edit
screen. Press
y
ã
‡
ä
£
100
¹
„
¡
¤
Í
to enter the expression to define the top half of
the circle,
Y
1
=
‡
(100–X
2
)
.
The bottom half of the circle is defined by
Y
2
=
M‡
(100–X
2
)
. However, on the TI
.
82 you can
define one function in terms of another, so to
define
Y
2
=
M
Y
1
, press
Ì
y
ã
Y
.
VARS
ä
(to display
the
Y=
variables menu)
1
(to select
Function...
)
1
(to select
Y
1
).
2. Press
q
and then select
ZStandard
. This is a
quick way to reset the
WINDOW
variables to the
standard values. It also graphs the functions; you
do not need to press
s
.
Notice that the functions appear as an ellipse in
the standard viewing window.
3. To adjust the display so each “dot” represents an
equal width and height, press
q
and then
select
ZSquare
. The functions are replotted and
now appear as a circle on the display.
4. To see the effect of
ZSquare
on the
WINDOW
variables, press
p
and notice the new
values for
Xmin
,
Xmax
,
Ymin
, and
Ymax
.
Function Graphing 3-3
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 3 of 24
Defining a Graph
To define a graph, you set the modes, enter and select the functions to graph,
and define the viewing WINDOW and WINDOW FORMAT. Once you have defined
a graph, you can plot, display, and explore it.
Steps in Defining a Graph
There are six basic steps to defining a graph. You may not need to do all the
steps each time you define a graph. The procedures are described in detail
on the following pages.
1. Set the
MODE
to
Func
graphing.
2. Enter or edit a function in the
Y=
list.
3. Select the
Y=
function you want to graph.
4. Define the viewing
WINDOW
variables.
5. Set the
WINDOW FORMAT
.
6. Deselect stat plots, if appropriate (Chapter 12.)
Exploring a Graph
Once you have defined a graph, you can display it and then use several
tools of the TI
.
82 to explore the behavior of the function or functions.
These tools are described later in this chapter.
Saving a Graph
You can store the elements that define the current graph in one of six graph
databases (Chapter 8). Later, you can recall that database to recreate the
current graph.
You can store a picture of the current graph display in one of six graph
pictures (Chapter 8). Later, you can superimpose that picture on the
current graph.
3-4 Function Graphing
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 4 of 24
Setting Graph Modes
Pressing
z
displays the current MODE settings (Chapter 1). The graphing
MODE in function graphing must be Func.
Checking and Changing Graphing Modes
Press
z
to display the
MODE
settings. The current settings are
highlighted.
The TI
.
82 has four graphing modes.
¦
Func
(function graphing)
¦
Par
(parametric graphing)
¦
Pol
(polar graphing)
¦
Seq
(sequence graphing)
To graph functions, you must select
Func
(function graphing). The basics
of graphing on the TI
.
82 are described in this chapter. Differences in
parametric graphing (Chapter 4), polar graphing (Chapter 5), and sequence
graphing (Chapter 6) are described in those chapters.
Radian
or
Degree
MODE
may affect how some functions are interpreted.
Connected
or
Dot
affects how the selected functions are plotted.
Sequential
or
Simul
affects how functions are plotted if you have more
than one function selected.
Setting Modes from a Program
You may set the graphing mode and other modes from a program.
Begin on a blank line in the program editor. Press
z
to display the
interactive
MODE
selection screen. Use
†
,
}
,
~
, and
|
to place the cursor
on the
MODE
that you want to select, and press
Í
. The name of the
MODE
is copied to the cursor location.
Function Graphing 3-5
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Defining Functions in the Y= List
Pressing
o
accesses the Y= edit screen, where you enter the functions to graph.
You can store up to ten functions in memory at one time. You can graph one or
more of these functions at a time.
Displaying the Functions in the Y= List
Press
o
to display the
Y=
edit screen. In the example below, the
Y
1
and
Y
2
functions are defined.
Defining a New Function
To define a new function, enter an expression on the
Y=
edit screen.
1. Move the cursor to the function in the
Y=
list you want to define. If
necessary, press
‘
to erase a previously entered function.
2. Enter the expression to define the function.
¦
You may use functions and variables (including matrices and lists) in
the expression. If the expression evaluates to a value that is not a
real number, that point is not plotted; an error does not occur.
¦
The independent variable in the function is
X
. You may press
„
,
rather than pressing
ƒ
ã
X
ä
, for the
X
variable. (
Func
MODE
defines the independent variable as
X
.)
¦
The expression is stored as one of the ten user-defined functions in
the
Y=
list as you enter it.
3. When you complete the expression, press
Í
to move to the
beginning of the next function.
3-6 Function Graphing
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Editing a Function
1. Move the cursor to the function in the
Y=
list you want to change.
2. Make the changes. You can press
‘
to erase the expression and
then enter a new expression.
The expression is stored as one of the ten user-defined functions in the
Y=
list as you enter it.
Clearing a Function
To clear or erase a function on the
Y=
edit screen, position the cursor
anywhere on the function, and then press
‘
.
Defining Functions from the Home Screen or a Program
1. Begin on a blank line. Press
ƒ
ã
"
ä
, enter the expression, and then
press
ƒ
ã
"
ä
again.
2. Press
¿
.
3. Press
y
ã
Y
.
VARS
ä
, select
Function...
, and then select the name of the
function, which is copied to the cursor location.
4. Press
Í
to complete the instruction.
"
expression
"
!
Y
n
When the instruction is executed, the TI
.
82 stores the expression to the
Y=
list, selects the function, and displays the message
Done
.
Evaluating Y= Functions in Expressions
You can the calculate the value of a
Y=
function at a specified value of
X
.
For example, if
Y
1
=.2X
3
–2X+6
:
Function Graphing 3-7
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Selecting Functions
Only functions that are selected are graphed. Up to ten functions may be selected
at one time.
Turning a Function “On” or “Off”
You select and deselect (“turn on” and “turn off”) functions on the
Y=
edit
screen. The = sign on a selected function is highlighted. To change the
selection status of a function:
1. If the
Y=
edit screen is not displayed, press
o
to display the functions.
2. Move the cursor to the function whose status you want to change.
3. Use
|
to place the cursor over the
=
sign of the function.
4. Press
Í
to change the status.
Note: When you enter or edit a function, it is selected automatically. When
you clear a function, it is deselected.
Leaving the Y= Edit Screen
To leave the
Y=
edit screen:
¦
Select another screen by pressing the appropriate key, such as
s
or
p
.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
Selecting Functions from the Home Screen or a Program
1. Begin on a blank line. Press
y
ã
Y
.
VARS
ä
and select
On/Off...
. The
ON/OFF
menu is displayed.
2. Select the instruction you want,
FnOn
or
FnOff
. It is copied to the
cursor location.
3. If you want to turn specific functions on or off, enter the number of the
function(s), separated by commas.
When the instruction is executed, the status of each function in the current
graph mode is set appropriately and
Done
is displayed.
FnOn
FnOff
FnOn
function1
,
function2
,
. . .
FnOff
function1
,
function2
,
. . .
For example, in
Func
MODE
,
FnOff:FnOn 1,3
turns off all functions in the
Y=
list and then turns on
Y
1
and
Y
3
.
3-8 Function Graphing
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Defining the Viewing
WINDOW
The WINDOW variables determine the boundaries and other attributes of the
viewing WINDOW. The WINDOW variables are shared by all graphing modes.
TI-82 Viewing WINDOW
The viewing
WINDOW
of the TI
.
82 is the portion of the coordinate plane
defined by
Xmin
,
Xmax
,
Ymin
, and
Ymax
. The distance between tick marks
is defined by
Xscl
for the
X
axis and
Yscl
for the
Y
axis.
Xmax
Ymin
Ymax
Xscl
Yscl
Xmin
Checking the Viewing WINDOW
Press
p
to display the current
WINDOW
variable values. The values
shown here are the standard values.
Changing a WINDOW Variable Value
1. Press
†
to move to the
WINDOW
variable you want to change.
2. To enter a real value (which can be an expression), you may do any of
the following:
¦
Position the cursor and then make the changes.
¦
Press
‘
to clear the value and then enter a new value.
¦
Begin entering a new value. The original value is cleared
automatically when you begin typing.
3. Press
Í
,
†
, or
}
. If you entered an expression, it is evaluated. The
new value is stored.
Xmin
must be less than
Xmax
and
Ymin
must be less than
Ymax
, or you will
get an error message when you press
s
. To turn off the tick marks, set
Xscl=0
or
Yscl=0
.
Function Graphing 3-9
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Leaving the WINDOW Edit Screen
To leave the
WINDOW
edit screen:
¦
Select another screen by pressing the appropriate key, such as
s
or
o
.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
Storing to a WINDOW Variable from the Home Screen or a Program
Begin on a blank line.
1. Enter the value you want to store (which can be an expression).
2. Press
¿
.
3. Press
to display the
VARS
menu.
4. Select
Window...
to display the
WINDOW
variables.
5. Select the
WINDOW
variable to which you want to store. The name of
the variable is copied to the cursor location where you are editing.
6. Press
Í
to complete the instruction.
When the instruction is executed, the TI
.
82 stores the value in the
WINDOW
variable.
Note: You can use a
WINDOW
variable in an expression by performing
steps 3, 4, and 5.
@
X and
@
Y
The variables
@
X
and
@
Y
define the distance between the centers of two
adjoining pixels on a graph (graphing accuracy).
(
Xmax
–
Xmin
)(
Ymax
–
Ymin
)
@
X
=
@
Y
=
94 62
@
X
and
@
Y
are not on the
WINDOW
screen; they are accessible through the
VARS Window
menu.
@
X
and
@
Y
are calculated from
Xmin
,
Xmax
,
Ymin
, and
Ymax
when a graph is displayed.
You can store values directly to
@
X
and
@
Y
, in which case
Xmax
and
Ymax
are calculated from
@
X
,
Xmin
,
@
Y
, and
Ymin
immediately.
3-10 Function Graphing
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Setting WINDOW FORMAT
WINDOW FORMAT determines how a graph appears on the display. WINDOW
FORMAT settings apply to all graphing modes.
Checking WINDOW FORMAT
To display the
WINDOW FORMAT
screen, press
p
~
. The current
settings are highlighted.
WINDOW FORMAT
RectGC PolarGC
Sets rectangular or polar cursor.
CoordOn CoordOff
Sets cursor coordinates on or off.
GridOff GridOn
Sets grid off or on.
AxesOn AxesOff
Sets axes on or off.
LabelOff LabelOn
Sets axes label off or on.
Changing WINDOW FORMAT
1. Move the cursor to the row of the setting you want to change. The
setting the cursor is on blinks.
2. Move the cursor to the setting you want and press
Í
.
RectGC, PolarGC
The cursor coordinate setting determines if the cursor location is displayed
(if
CoordOn
) as rectangular coordinates
X
and
Y
or polar coordinates
R
and
q
. It also determines which variables are updated. In
RectGC
(rectangular graphing coordinates)
FORMAT
, plotting the graph, moving
the free-moving cursor, or tracing updates and displays
X
and
Y
. In
PolarGC
(polar graphing coordinates)
FORMAT
,
X
,
Y
,
R
, and
q
are updated, and
R
and
q
are displayed.
CoordOn, CoordOff
CoordOn
(coordinates on) displays the function number in the upper-right
corner and the cursor coordinates at the bottom of the graph.
CoordOff
(coordinate off) does not display the function number or the coordinates
for the free-moving cursor or during
TRACE
.
GridOff, GridOn
Grid points correspond to the axis tick marks.
GridOff
does not display grid
points.
GridOn
does display the grid points.
AxesOn, AxesOff
AxesOn
displays the axes.
AxesOff
does not display the axes. It overrides
the Axis Label setting.
LabelOff, LabelOn
LabelOn
and
LabelOff
determine whether to display a label for the axes (
X
and
Y
).
Function Graphing 3-11
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Displaying a Graph
Pressing
s
graphs any functions selected on the Y= edit screen. The current
MODE settings apply, and the current values of the WINDOW variables define the
viewing WINDOW.
Displaying a New Graph
Press
s
to display the graph of the selected function or functions.
(Some operations, such as
TRACE
and the
ZOOM CALC
operations, display
the graph automatically.) As a graph is plotted, the busy indicator is on and
X
and
Y
are updated.
Pausing a Graph
Note: While a graph is being plotted, you can:
¦
Press
Í
to pause graphing, then press
Í
to resume plotting.
¦
Press
É
to stop graphing, then press
s
to start over.
Smart Graph
When you press
s
, Smart Graph displays the graph screen
immediately if nothing has changed that requires the functions to be
replotted since the last time the graph was displayed.
If you have not changed any of the following since the graph was last
displayed, Smart Graph displays the graph immediately. If you have
changed one or more of these, pressing
s
replots the graph based on
the new values.
¦
Changed a
MODE
setting that affects graphs.
¦
Changed a function.
¦
Selected or deselected a function.
¦
Changed the value of a variable in a selected function.
¦
Changed a
WINDOW
variable or a
FORMAT
setting.
¦
Cleared drawings by selecting
ClrDraw
(Chapter 8).
¦
Changed a
STAT PLOT
definition (Chapter 12).
3-12 Function Graphing
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Graphing a Family of Curves
If you enter a list (Chapter 11) as an element in an expression, the TI
.
82
plots the function for each value in the list, graphing a family of curves. (In
Simul
, it graphs all functions for the first element, and so on.)
{2,4,6}sin X
graphs three functions:
2 sin X
,
4 sin X
, and
6 sin X
.
{2,4,6}sin {1,2,3}X
graphs
2 sin X
,
4 sin 2X
, and
6 sin 3X
.
Function Graphing 3-13
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Exploring a Graph with the Free-Moving Cursor
While a graph is displayed, you can move the free-moving cursor anywhere on
the graph and display the coordinates of any location on the graph.
Free-Moving Cursor
You can use
|
,
~
,
}
, or
†
to move the cursor around the graph. When you
first display the graph, no cursor is visible. As soon as you press
|
,
~
,
}
,
or
†
, the cursor moves from the center of the viewing window.
As you move the cursor around the graph, the coordinate values of the
cursor location are displayed at the bottom of the screen (if
CoordOn
).
Coordinate values generally appear in normal floating-decimal format. The
numeric display settings on the
MODE
screen do not affect coordinate
display.
To see the graph without the cursor or coordinate values, press
‘
or
Í
. When you press
|
,
~
,
}
, or
†
, the cursor moves from same
position.
Graphing Accuracy
The free-moving cursor moves from dot to dot on the screen. When you
move the cursor to a dot that appears to be “on” the function, it may be
near, but not on, the function; therefore, the coordinate value displayed at
the bottom of the screen is not necessarily a point on the function. To move
the cursor along a function, use
TRACE
(page 3
.
14).
The display coordinate values of the free-moving cursor approximate actual
math coordinates accurate to within the width/height of the dot. As
Xmin
and
Xmax
(and
Ymin
and
Ymax
) get closer together (after a
Zoom In
, for
example), graphing accuracy increases, and the coordinate values more
closely approximate the math coordinates.
)
Free-moving cursor “on” the curve
3-14 Function Graphing
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Exploring a Graph with TRACE
TRACE moves the cursor from one plotted point to the next along a function,
while displaying the cursor coordinates at the bottom of the screen.
Beginning a Trace
Press
r
to begin a trace. If the graph is not displayed already, the TI
.
82
displays it. The cursor is on the first selected function in the
Y=
list at the
middle
X
value on the screen. The number of the function shows at the
upper right of the display.
Moving along a Function
~
and
|
move the cursor along the function. Each press moves the cursor
from one plotted point to the next.
y
~
and
y
|
move the cursor five
plotted points at a time. The
Y
value is calculated from the
X
value; that is,
Y
=
Y
n
(X)
. If the function is undefined at an
X
value, the
Y
value is blank.
)
TRACE
cursor on the curve.
If the
Y
value of a function is above or below the viewing window, the
cursor disappears as you move it to that portion of the function; however,
the coordinate values at the bottom of the screen indicate the cursor
coordinates.
Panning to the Left or Right
If you trace a function off the left or right edge of the screen, the viewing
window automatically pans to the left or right.
Xmin
and
Xmax
are updated
to correspond to the new viewing window.
QuickZoom
While tracing, you can press
Í
to adjust the viewing
WINDOW
so that
the cursor location becomes the center of the new viewing
WINDOW
, even
if the cursor is above or below the display. This allows “panning” up and
down. After QuickZoom, the cursor remains in
TRACE
.
Function Graphing 3-15
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Moving from Function to Function
To trace another selected function on the graph, use
†
or
}
to move the
cursor to that function. The cursor movement is based on the order of the
selected functions in the
Y=
list, not the appearance of the functions as
graphed on the screen. The cursor moves to the new function at the same
X
value. The function number in the upper right corner of the display
changes.
Leaving TRACE
To leave
TRACE
:
¦
Select another screen by pressing the appropriate key, such as
p
or
q
.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
The
TRACE
cursor remains in the same location if you leave
TRACE
and
return, if Smart Graph has not caused the graph to be replotted.
Using TRACE in a Program
On a blank line in the program editor, press
r
. The instruction
Trace
is
copied to the cursor location. When the instruction is encountered during
program execution, the graph is displayed with the
TRACE
cursor on the
first selected function. As you trace, the cursor coordinate values are
updated. When you are done tracing functions, press
Í
to resume
program execution.
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Exploring a Graph with ZOOM
Pressing
q
accesses a menu that allows you to adjust the viewing WINDOW
of the graph quickly in a variety of ways. All of the ZOOM commands are
accessible from programs.
ZOOM Menu
ZOOM MEMORY
1: ZBox
Draws box to define viewing
WINDOW
.
2: Zoom In
Magnifies graph around cursor.
3: Zoom Out
Views more of graph around cursor.
4: ZDecimal
Sets .1 as dot size.
5: ZSquare
Sets equal sized dots on
X
and
Y
axes.
6: ZStandard
Sets standard
WINDOW
variables.
7: ZTrig
Sets built-in trig
WINDOW
variables.
8: ZInteger
Sets integer values on
X
and
Y
axes.
9: ZoomStat
Sets values for current lists.
ZBox
ZBox
lets you use the cursor to select opposite corners of a box to define a
new viewing
WINDOW
.
1. Select
ZBox
from the
ZOOM
menu. The different cursor at the center of
the screen indicates that you are using a
ZOOM
instruction.
2. Move the cursor to any corner of the box you want to define and then
press
Í
. As you move the cursor away from the point just selected,
you see a small square dot, indicating that the first corner is selected.
3. Move the cursor to the diagonal corner of the box you want to define.
As you move the cursor, the boundaries of the box change on the
screen.
Note: You can cancel
ZBox
any time before you press
Í
by
pressing
‘
.
4. When the box is defined as you want it, press
Í
to replot the graph.
You can repeat steps 2 through 4 to do another
ZBox
. To cancel
ZBox
,
press
‘
.
Function Graphing 3-17
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Zoom In, Zoom Out
Zoom In
magnifies the graph around the cursor location.
Zoom Out
displays a greater portion of the graph, centered on the cursor location, to
provide a more global view. The
XFact
and
YFact
settings determine the
extent of the zoom.
1. After checking or changing
XFact
and
YFact
(page 3
.
20), select
Zoom In
from the
ZOOM
menu.
Notice the different cursor. It indicates that you are using a
ZOOM
instruction.
2. Move the cursor to the point that you want as the center of the new
viewing
WINDOW
, then press
Í
.
The TI
.
82 adjusts the viewing
WINDOW
by
XFact
and
YFact
, updates
the
WINDOW
variables, and replots the selected functions, centered on
the cursor location.
3. To zoom in on the graph again:
¦
To zoom in at the same point, press
Í
.
¦
To zoom in at a new point, move the cursor to the point that you
want as the center of the new viewing
WINDOW
and then press
Í
.
Zoom Out
The procedure for
Zoom Out
is the same as for
Zoom In
.
Leaving Zoom In or Zoom Out
To leave
Zoom In
or
Zoom Out
:
¦
Select another screen by pressing the appropriate key, such as
r
or
s
.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
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ZDecimal
ZDecimal
replots the functions immediately, updating the
WINDOW
variables to preset values that set
@
X
and
@
Y
equal to
.1
and defining the
X
and
Y
value of each pixel as one decimal.
Xmin =
M
4.7 Ymin =
M
3.1
Xmax = 4.7 Ymax = 3.1
Xscl = 1 Yscl = 1
ZSquare
ZSquare
replots the functions immediately, redefining the
WINDOW
based
on the current
WINDOW
variables, but adjusted in only one direction so
that
@
X=
@
Y
. This makes the graph of a circle look like a circle.
Xscl
and
Yscl
remain unchanged. The midpoint of the current graph (not the
intersection of the axes) becomes the midpoint of the new graph.
ZStandard
ZStandard
replots the functions immediately, updating the
WINDOW
variables to the standard values:
Xmin =
M
10 Ymin =
M
10
Xmax = 10 Ymax = 10
Xscl = 1 Yscl = 1
ZTrig
ZTrig
replots the functions immediately, updating the
WINDOW
variables to
preset values appropriate for trig plotting functions. In
Radian
MODE
these
are:
Xmin =
M
(47
à
24)
p
Ymin =
M
4
Xmax = (47
à
24)
p
Ymax = 4
Xscl =
p
/2 Yscl = 1
ZInteger
ZInteger
redefines the viewing
WINDOW
so
@
X=1
and
@
Y=1
,
Xscl=10
, and
Yscl=10
, replotting the functions after you move the cursor to the point that
you want as the center of the new
WINDOW
and press
Í
.
ZoomStat
ZoomStat
redefines the viewing
WINDOW
so that all statistical data points
are displayed. For one-variable plots (histograms and box plots), only
Xmin
and
Xmax
are adjusted. If the top of the histogram is not shown, use
TRACE
to determine the value for
Ymax
.
Function Graphing 3-19
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Using ZOOM MEMORY
ZPrevious allows you to return to the WINDOW displayed prior to the previous
ZOOM. ZoomSto stores the values of the current WINDOW variables to user-
defined ZOOM MEMORY variables. ZoomRcl changes the WINDOW to the values
stored with ZoomSto.
ZOOM MEMORY Menu
ZOOM MEMORY
1: ZPrevious
Uses previous viewing
WINDOW
.
2: ZoomSto
Stores user-defined
WINDOW
.
3: ZoomRcl
Recalls user-defined
WINDOW
.
4: SetFactors
…
Changes
Zoom In
,
Zoom Out
factors.
ZPrevious
When you select
ZPrevious
from the
ZOOM MEMORY
menu, the graph is
replotted using the
WINDOW
variables of the graph displayed prior to the
previous
ZOOM
that you did.
ZoomSto
To store the current viewing
WINDOW
, select
ZoomSto
from the
ZOOM MEMORY
menu. The graph is displayed if necessary, and the values
of the current
WINDOW
variables are stored in the user-defined
ZOOM
variables:
ZXmin
,
ZXmax
,
ZXscl
,
ZYmin
,
ZYmax
, and
ZYscl
. The action is
immediate, there is no prompting on the display.
These variables are global; they apply to all graphing modes. For example,
changing the value of
ZXmin
in
Func
MODE
also changes it in
Par
MODE
.
The user-defined
WINDOW
variables contain the standard values until you
store to them the first time.
ZoomRcl
To view the selected graphing functions in the user-defined
WINDOW
,
select
ZoomRcl
from the
ZOOM MEMORY
menu. The
WINDOW
variables
are updated with the user-defined values, and the graph is plotted.
Using ZOOM MEMORY from the Home Screen or a Program
From the Home screen or a program, you can store directly to any of the
user-defined
ZOOM
variables.
From a program, you can select the
ZoomSto
or
ZoomRcl
instructions from
the
ZOOM MEMORY
menu.
3-20 Function Graphing
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 20 of 24
Setting ZOOM FACTORS
The ZOOM FACTORS, XFact and YFact, determine the extent of the change for
the viewing window created by Zoom In or Zoom Out on a graph.
ZOOM FACTORS
ZOOM FACTORS
are positive numbers (not necessarily integers) greater
than or equal to 1. They define the magnification or reduction factor used
to
Zoom In
or
Zoom Out
around a point.
Checking XFact and YFact
To review the current values of
XFact
and
YFact
, select
SetFactors...
from
the
ZOOM MEMORY
menu. The
ZOOM FACTORS
screen appears (the
values shown are the standard values).
Changing XFact and YFact
To change
XFact
or
YFact
:
¦
Enter a new value. The original value is cleared automatically when you
begin typing.
¦
Position the cursor over the digit you want to change. Then type over it
or use
{
to delete it.
Leaving ZOOM FACTORS
To leave
ZOOM FACTORS
:
¦
Select another screen by pressing the appropriate key, such as
p
or
q
.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
Function Graphing 3-21
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 21 of 24
Using CALC (Calculate) Operations
Pressing
y
ã
CALC
ä
(above
r
) accesses a menu with operations you can use
to analyze the current graph functions. You are prompted to specify the
function(s), interval, and point.
CALCULATE Menu
CALCULATE
1: value
Calculates function value for given
X
.
2: root
Finds root of function.
3: minimum
Finds minimum of function.
4: maximum
Finds maximum of function.
5: intersect
Finds intersection of functions.
6: dy/dx
Finds numeric derivative of function.
7:
‰
f(x)dx
Finds numeric integral of function.
value
value
evaluates currently selected functions for a specified value of
X
.
1. Select
value
from the
CALC
menu. The current graph is displayed, with
a prompt for you to enter
X
.
2. Enter a real value for
X
between
Xmin
and
Xmax
(which can be an
expression). Note: When there is a value entered for
X
,
‘
clears
the value; when there is no value,
‘
cancels
value
.
3. Press
Í
. The result cursor is on the first selected function in the list
at the entered
X
and the coordinate values are displayed (even if you
have selected
CoordOff
on the
WINDOW FORMAT
screen).
4. Press
†
or
}
to move the cursor between functions at the entered
X
value. When
|
or
~
are pressed, the free-moving cursor appears. It
cannot necessarily move back to the
X
value.
3-22 Function Graphing
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 22 of 24
root
root
(
CALC
item
2
) uses
solve(
(Chapter 2) to find the root (zero or
X
-intercept) of a function. Selecting good values for the bounds and a guess
help it find the correct root and find it more quickly.
1. Select
root
from the
CALC
menu. The current graph is displayed, with a
prompt to enter
Lower Bound
.
2. Use
†
or
}
to move the cursor to the function for which you want to
find the root.
3. Move the cursor to the
X
value you want for the lower bound of the
interval and press
Í
. A
4
indicator at the top of the display shows
the lower bound.
4. Set the upper bound in the same way. An indicator shows the upper
bound.
5. You are prompted for a
Guess
to help the TI
.
82 find the correct root
and to find it more quickly.
6. Use
|
or
~
to move the cursor to a point near the root of the function,
between the bounds. Press
Í
.
The result cursor is on the solution and the coordinate values are displayed
(even if you have selected
CoordOff
on the
WINDOW FORMAT
screen).
When you press
|
,
~
,
}
, or
†
, the free-moving cursor appears.
Function Graphing 3-23
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 23 of 24
minimum, maximum
minimum
(
CALC
item
3
) and
maximum
(
CALC
item
4
) find the minimum or
maximum of a function in a specified interval to a tolerance of 1
E
L
5.
1. Select
minimum
or
maximum
from the
CALC
menu. The current graph
is displayed.
2. Set
Lower Bound
,
Upper Bound
, and
Guess
as described for
root
.
The result cursor is on the solution and the coordinate values are displayed
(even if you have selected
CoordOff
on the
WINDOW FORMAT
screen).
When you press
|
,
~
,
}
, or
†
, the free-moving cursor appears.
intersect
intersect
(
CALC
item
5
) uses
solve(
(Chapter 2) to find the intersection of
two functions. The intersection must appear on the display.
1. Select
intersection
from the
CALC
menu. The current graph is displayed
and you are prompted to select the
First curve
.
2. Use
†
or
}
to move the cursor to the first function and press
Í
.
3. Use
†
or
}
to move the cursor to the second function and press
Í
.
The result cursor is on the solution and the coordinate values are displayed
(even if you have selected
CoordOff
on the
WINDOW FORMAT
screen).
When you press
|
,
~
,
}
, or
†
, the free-moving cursor appears.
3-24 Function Graphing
8203FUNC.DOC TI-82, Chapter 3, English Bob Fedorisko Revised: 02/09/01 9:06 AM Printed: 02/09/01
12:36 PM Page 24 of 24
dy/dx
dy/dx
(numerical derivative,
CALC
item
6
) finds the numerical derivative
(slope) of a function at a point with
H
= 1
E
L
3.
1. Select
dy/dx
from the
CALC
menu. The current graph is displayed.
2. Move the cursor to the
X
value at which you want to calculate the
derivative and press
Í
.
The result cursor is on the solution and the coordinate values are displayed
(even if you have selected
CoordOff
on the
WINDOW FORMAT
screen).
When you press
|
,
~
,
}
, or
†
, the free-moving cursor appears.
‰
f(x)dx
‰
f(x)dx
(numerical integral,
CALC
item
7
) finds the numerical integral of a
function a specified interval. It uses the
fnInt(
function, with a tolerance of
1
E
L
3.
1. Select
‰
f(x)dx
from the
CALC
menu. The current graph is displayed, with
a prompt to enter
Lower Bound
.
2. Use
†
or
}
to move the cursor to the function for which you want to
calculate the integral.
3. Set
Lower Limit
and
Upper Limit
as described for
root
.
The integral value is displayed and the integrated area is shaded. When you
press
|
,
~
,
}
, or
†
, the free-moving cursor appears.
Note: The shaded area is a drawing. Use
ClrDraw
or any change that
invokes Smart Graph to clear the shaded area. (Chapter 8)
Parametric Graphing 4-1
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 1 of 6
Chapter 4: Parametric Graphing
This chapter describes how to graph parametric equations on the TI
.
82. Before
doing parametric graphing, you should be familiar with Chapter 3, Function
Graphing.
Chapter Contents
Getting Started: Path of a Ball
.....................
4-2
Defining and Displaying a Parametric Graph
...........
4-3
Exploring a Parametric Graph
.....................
4-6
4-2 Parametric Graphing
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 2 of 6
Getting Started: Path of a Ball
Getting Started is a fast-paced introduction. Read the chapter for details.
Graph the parametric equation that describes the position of a ball kicked at an
angle of 60
¡
with an initial velocity of 15 meters per second. (Ignore air
resistance.) What is the maximum height? When does the ball strike the ground?
1. Press
z
. Press
†
†
†
~
Í
to select
Par
MODE
.
For initial velocity v
0
and angle
q
, the horizontal
component of the position of the ball as a
function of time is X(t)=tv
0
cos
q
. The vertical
component is Y(t)=tv
0
sin
q
–(g
à
2)t
2
. The gravity
constant g is 9.8 m/sec
2
.
2. Press
o
. Press
15
„
™
60
y
ã
ANGLE
ä
1
(to select
¡
)
Í
to define the
X
portion of the
parametric equation in terms of
T
.
3. Press
15
„
˜
60
y
ã
ANGLE
ä
1
(to select
¡
)
¹
£
9.8
¥
2
¤
„
¡
Í
to define the
Y
portion.
4. Press
p
. Press
†
to move to
Tmin
and
then enter the
WINDOW
variables appropriate
for this problem.
Tmin=0 Xmin=-2 Ymin=-2
Tmax=3 Xmax=25 Ymax=10
Tstep=.02 Xscl=5 Yscl=5
5. Press
r
to graph the position of the ball as
a
function of time.
Tracing begins at
Tmin
. As you press
~
to trace
the curve, the cursor follows the path of the ball
over time. The values for
X
(distance),
Y
(height), and
T
(time) are displayed at the
bottom of the screen.
Parametric Graphing 4-3
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 3 of 6
Defining and Displaying a Parametric Graph
Parametric equations consist of an X component and a Y component, each
expressed in terms of the same independent variable T. They are often used to
graph equations over time. Up to six pairs of parametric equations can be defined
and graphed at a time.
Defining a Parametric Graph
The steps for defining a parametric graph are the same as those for defining
a function graph. Differences are noted below.
Setting Parametric Graph Modes
Press
z
to display the
MODE
settings. To graph parametric equations,
you must select
Par
before you enter
WINDOW
variables or enter the
components of parametric equations. Also, you usually should select
Connected
to obtain a more meaningful
Par
graph.
Displaying Parametric Equations
After selecting
Par
MODE
, press
o
to display the parametric
Y=
edit
screen.
On this screen, you display and enter both
X
and
Y
components. TI
.
82 has
six equations, each defined in terms of
T
.
Defining Parametric Equations
Follow the same procedures as for
Func
graphing to enter the two
components that define a new parametric equation.
¦
You must define both the
X
and
Y
components in a pair.
¦
The independent variable in each component is
T
. You may press
„
,
rather than pressing
ƒ
ã
T
ä
, to enter the parametric variable
T
. (
Par
MODE
defines the independent variable as
T
.)
4-4 Parametric Graphing
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 4 of 6
Selecting Parametric Equations
Only the selected parametric equations are graphed. The
=
sign on both
components of selected equations is highlighted. You may select any or all
of the equations on the parametric
Y=
edit screen.
To change the selection status of a parametric equation, press
|
to move
the cursor onto the
=
sign on either the
X
or
Y
component and press
Í
.
The status on both the
X
and
Y
components is changed.
Note: When you enter both components of an equation or edit either
component, that equation is selected automatically.
Setting WINDOW Variables
Press
p
to display the current
WINDOW
variable values. The
WINDOW
variables define the viewing
WINDOW
. The values shown are the
standard values in
Radian
MODE
.
Tmin=0
Smallest
T
value to evaluate
Tmax=6.2831853
…
Largest
T
value to evaluate (2
p
)
Tstep=.1308996
…
T
value increment (
pà
24)
Xmin=-10
Smallest
X
value to be displayed
Xmax=10
Largest
X
value to be displayed
Xscl=1
Spacing between
X
tick marks
Ymin=-10
Smallest
Y
value to be displayed
Ymax=10
Largest
Y
value to be displayed
Yscl=1
Spacing between
Y
tick marks
You may want to change the
T
WINDOW
variable values to ensure that
sufficient points are plotted.
Parametric Graphing 4-5
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 5 of 6
Setting the WINDOW FORMAT
Press
p
~
to display the current
WINDOW FORMAT
settings. The
formats are shared with the other graphing modes.
Displaying a Graph
When you press
s
, the TI
.
82 plots the selected parametric equations.
It evaluates both the
X
and the
Y
component for each value of
T
(from
Tmin
to
Tmax
in intervals of
Tstep
) and then plots each point defined by
X
and
Y
.
The
WINDOW
variables define the viewing
WINDOW
.
As a graph is plotted, the TI
.
82 updates
X
,
Y
, and
T
.
Smart Graph applies to parametric graphs.
WINDOW Variables and Y-VARS Menus
From the Home screen, you can:
¦
Access functions by using the name of the component of the equation
as a variable.
¦
Select or deselect parametric equations from a program.
¦
Store parametric equations.
¦
Store values directly to
WINDOW
variables.
4-6 Parametric Graphing
8204PARA.DOC TI-82, Chapter 4, English Bob Fedorisko Revised: 02/09/01 9:08 AM Printed: 02/09/01
12:37 PM Page 6 of 6
Exploring a Parametric Graph
As in Function graphing, three tools are available for exploring a graph: using the
free-moving cursor, tracing an equation, and zooming.
Free-Moving Cursor
The free-moving cursor works in
Par
graphing just as it does in
Func
graphing. In
RectGC
FORMAT
, moving the cursor updates and displays (if
FORMAT
is
CoordOn
) the values of
X
and
Y
. (In
PolarGC
FORMAT
,
X
,
Y
,
R
,
and
q
are updated, and
R
and
q
are displayed.)
TRACE
TRACE
lets you move the cursor along the equation one
Tstep
at a time.
When you begin a trace, the cursor is on the first selected equation at
Tmin
.
The number of the equation shows in the upper right of the display.
In
RectGC
FORMAT
,
TRACE
updates and displays (if
FORMAT
is
CoordOn
)
the values of
X
,
Y
, and
T
. (In
PolarGC
FORMAT
,
X
,
Y
,
R
,
q
and
T
are
updated, and
R
,
q
, and
T
are displayed.) The
X
and
Y
(or
R
and
q
) values are
calculated from
T
.
If the cursor moves off the top or bottom of the screen, the coordinate
values at the bottom of the screen continue to change appropriately.
y
|
and
y
~
move the
TRACE
cursor five plotted points at a time. The
TRACE
cursor remains in the same location if you leave
TRACE
and return,
if Smart Graph has not caused the graph to be replotted.
QuickZoom is available in
Par
graphing, but panning is not.
ZOOM
ZOOM
operations work in
Par
graphing as they do in
Func
graphing. Only
the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
)
WINDOW
variables are affected.
T
WINDOW
variables (
Tmin
,
Tmax
, and
Tstep
) are
not affected, except when you select
ZStandard
(
Tmin
= 0,
Tmax
= 2
p
, and
Tstep
=
pà
24).
ZOOM MEMORY
variables in
Par
graphing include
ZTmin
,
ZTmax
, and
ZTstep
.
CALC
CALC
operations work in
Par
graphing as they do in
Func
graphing.
CALC
operations available in
Par
graphing are
value
,
dy/dx
,
dy/dt
, and
dx/dt
.
Polar Graphing 5-1
8205POLR.DOC TI-82, Chapter 5, English Bob Fedorisko Revised: 02/09/01 9:09 AM Printed: 02/09/01
12:37 PM Page 1 of 6
Chapter 5: Polar Graphing
This chapter describes how to graph polar equations on the TI
.
82. Before doing
polar graphing, you should be familiar with Chapter 3, Function Graphing.
Chapter Contents
Getting Started: Polar Rose
.....................
5
-
2
Defining and Displaying a Polar Graph
.............
5
-
3
Exploring a Polar Graph
.......................
5
-
6
5-2 Polar Graphing
8205POLR.DOC TI-82, Chapter 5, English Bob Fedorisko Revised: 02/09/01 9:09 AM Printed: 02/09/01
12:37 PM Page 2 of 6
Getting Started: Polar Rose
Getting Started is a fast-paced introduction. Read the chapter for details.
The polar equation A sin B
q
graphs a rose. Graph the rose for A=8 and B=2.5, and
then explore the appearance of the rose for other values of A and B.
1. Press
z
. Press
†
†
†
~
~
Í
to select
Pol
MODE
. Choose the initial settings for the
other modes (the choice at the beginning of
each line).
2. Press
o
to display the polar
Y=
edit screen.
Press
8
˜
2.5
„
Í
to define
r
1
.
3. Press
q
6
to select
ZStandard
to graph the
equation in the standard viewing
WINDOW
.
Notice that the graph shows only five petals of
the rose and that the rose does not appear
symmetrical. This is because the standard
WINDOW
defines the
WINDOW
(rather than the
pixels) as square and sets
q
max=2
p
.
4. Press
p
to display the
WINDOW
settings.
Press
†
†
4
y
ã
p
ä
to increase the value of
q
max
.
5. Press
q
5
to select
ZSquare
and plot the
graph.
6. Continue, changing
A
and
B
to other values.
Polar Graphing 5-3
8205POLR.DOC TI-82, Chapter 5, English Bob Fedorisko Revised: 02/09/01 9:09 AM Printed: 02/09/01
12:37 PM Page 3 of 6
Defining and Displaying a Polar Graph
Polar equations are defined in terms of the independent variable
q
. Up to six polar
equations can be defined and graphed at a time.
Defining a Polar Graph
The steps for defining a polar graph are the same as those for defining a
function graph. Differences are noted below.
Setting Polar Graph Modes
Press
z
to display the
MODE
settings. To graph polar equations, you
must select
Pol
before you enter
WINDOW
variables or enter a polar
equation. Also, you usually should select
Connected
to obtain a more
meaningful
Pol
graph.
Displaying Polar Equations
After selecting
Pol
MODE
, press
o
to display the polar
Y=
edit screen.
On this screen, you display and enter polar equations. The TI
.
82 has six
equations, each defined in terms of
q
.
Defining Polar Equations
Follow the same procedures as for
Func
graphing to define a new polar
equation. The independent variable in a polar equation is
q
. You may press
„
, rather than pressing
ƒ
ã
q
ä
, to enter the polar variable
q
.
(
Pol
MODE
defines the independent variable as
q
.)
Selecting Polar Equations
Only the selected polar equations are graphed. The
=
sign on selected
equations is highlighted. You may select any or all of the equations on the
polar
Y=
edit screen.
To change the selection status of a polar equation, press
|
to move the
cursor onto the
=
sign and press
Í
.
Note: When you edit an equation, that equation is selected automatically.
5-4 Polar Graphing
8205POLR.DOC TI-82, Chapter 5, English Bob Fedorisko Revised: 02/09/01 9:09 AM Printed: 02/09/01
12:37 PM Page 4 of 6
Setting WINDOW Variables
Press
p
to display the current
WINDOW
variable values. The
WINDOW
variables define the viewing
WINDOW
. The values shown are the
standard values in
Radian
MODE
.
q
min=0
Smallest
q
value to be evaluated
q
max=6.2831853
…
Largest
q
value to evaluate (2
p
)
q
step=.1308996
…
Increment between
q
values (
pà
24)
Xmin=-10
Smallest
X
value to be displayed
Xmax=10
Largest
X
value to be displayed
Xscl=1
Spacing between
X
tick marks
Ymin=-10
Smallest
Y
value to be displayed
Ymax=10
Largest
Y
value to be displayed
Yscl=1
Spacing between
Y
tick marks
You may want to change the
q
WINDOW
variable values to ensure that
sufficient points are plotted.
Setting the WINDOW FORMAT
Press
p
~
to display the current
WINDOW
FORMAT
settings. The
formats are shared with the other graphing modes.
Polar Graphing 5-5
8205POLR.DOC TI-82, Chapter 5, English Bob Fedorisko Revised: 02/09/01 9:09 AM Printed: 02/09/01
12:37 PM Page 5 of 6
Displaying a Graph
When you press
s
, the TI
.
82 plots the selected polar equations. It
evaluates
R
for each value of
q
(from
q
min
to
q
max
in intervals of
q
step
)
and then plots each point.
As a graph is plotted, the TI
.
82 updates
X
,
Y
,
R
, and
q
.
Smart Graph applies to polar graphs.
Note that the free-moving cursor displays
X
and
Y
coordinate values if the
WINDOW FORMAT
setting is the default
RectGC
. To see
R
and
q
, select
PolarGC
WINDOW FORMAT
.
WINDOW Variables and Y-VARS Menus
From the Home screen, you can:
¦
Access functions by using the name of the equation as a variable.
¦
Select or deselect polar equations from a program.
¦
Store polar equations.
¦
Store values directly to
WINDOW
variables.
5-6 Polar Graphing
8205POLR.DOC TI-82, Chapter 5, English Bob Fedorisko Revised: 02/09/01 9:09 AM Printed: 02/09/01
12:37 PM Page 6 of 6
Exploring a Polar Graph
As in function graphing, three tools are available for exploring a graph: using the
free-moving cursor, tracing an equation, and zooming.
Free-Moving Cursor
The free-moving cursor works in
Pol
graphing just as it does in
Func
graphing. In
RectGC
FORMAT
, moving the cursor updates and displays (if
FORMAT
is
CoordOn
) the values of
X
and
Y
. (In
PolarGC
FORMAT
,
X
,
Y
,
R
,
and
q
are updated, and
R
and
q
are displayed.)
TRACE
TRACE
lets you move the cursor along the equation one
q
step
at a time.
When you begin a trace, the cursor is on the first selected equation at
q
min
.
The number of the equation shows in the upper right of the display.
In
RectGC
FORMAT
,
TRACE
updates and displays (if
FORMAT
is
CoordOn
)
the values of
X
,
Y
, and
q
. (In
PolarGC
FORMAT
,
X
,
Y
,
R
, and
q
are updated,
and
R
and
q
are displayed.)
If the cursor moves off the top or bottom of the screen, the coordinate
values at the bottom of the screen continue to change appropriately.
y
|
and
y
~
move the
TRACE
cursor five plotted points at a time. The
TRACE
cursor remains in the same location if you leave
TRACE
and return,
if Smart Graph has not caused the graph to be replotted.
QuickZoom is available in
Pol
graphing, but panning is not.
ZOOM
ZOOM
operations work in
Pol
graphing as they do in
Func
graphing. Only
the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
)
WINDOW
variables are affected. The
q
WINDOW
variables (
q
min
,
q
max
, and
q
step
)
are not affected, except when you select
ZStandard
(
q
min
= 0,
q
max
= 2
p
,
and
q
step
=
pà
24). The
ZOOM MEMORY
variables in
Pol
graphing include
Z
q
min
,
Z
q
max
, and
Z
q
step
.
CALC
CALC
operations work in
Pol
graphing as they do in
Func
graphing. The
CALC
operations available in
Pol
graphing are
value
,
dy/dx
, and
dr/d
q
.
Sequence Graphing 6-1
8206SEQ.DOC TI-82, Chapter 6, English Bob Fedorisko Revised: 02/09/01 12:49 PM Printed: 02/09/01
12:50 PM Page 1 of 6
Chapter 6: Sequence Graphing
This chapter describes how to graph sequences on the TI
.
82. Before doing
sequence graphing, you should be familiar with Chapter 3, Function Graphing.
Chapter Contents
Getting Started: Forest and Trees
...................
6-2
Defining and Displaying a Sequence Graph
............
6-3
Exploring a Sequence Graph
......................
6-6
6-2 Sequence Graphing
8206SEQ.DOC TI-82, Chapter 6, English Bob Fedorisko Revised: 02/09/01 12:49 PM Printed: 02/09/01
12:50 PM Page 2 of 6
Getting Started: Forest and Trees
Getting Started is a fast-paced introduction. Read the chapter for details.
A small forest contains 4000 trees. The new forestry plan is that each year 20% of
the trees will be harvested and 1000 new trees will be planted. Will the forest
disappear? Does it stabilize at a certain number of trees? If so, what is that
number?
1. Press
z
. Press
†
†
†
~
~
~
Í
to
select
Seq
MODE
. Press
†
~
Í
to select
Dot
MODE
.
2. Press
o
. Each year the number of trees is 80
percent of what was there at the end of the prior
year. Press
~
2
(to select
iPart
, because
the company will not harvest part of a tree)
£
.8
y
ã
U
n-1
ä
(
2nd
function of
¬
)
¤
to define the
number of trees after each harvest. Press
Ã
1000
to define the replacement trees.
3. Press
p
. Press
†
to move to
U
n
Start
.
Press
4000
Í
to define the number of trees
at the beginning of the program.
4. Press
†
†
†
50
Í
to set
n
Max=50
to plot
the size of the forest over 50 years.
5. Set the other
WINDOW
variables:
Xmin=0 Ymin=0
Xmax=50 Ymax=6000
Xscl=10 Yscl=1000
6. Press
r
. Tracing begins at
n
Min
(before the
forestry program began). Press
~
to trace the
values year-by-year. The values for
n
(year) and
U
n
(trees) are displayed at the bottom of the
screen. How many years does it take to stabilize
the size of the forest?
Sequence Graphing 6-3
8206SEQ.DOC TI-82, Chapter 6, English Bob Fedorisko Revised: 02/09/01 12:49 PM Printed: 02/09/01
12:50 PM Page 3 of 6
Defining and Displaying a Sequence Graph
There are two sequence functions, U
n
and V
n
. Sequence functions can be
defined in terms of the independent variable (
n
) or the prior item in the sequence
function (U
n-1
or V
n-1
). They also can be defined in terms of the prior term in the
other sequence function.
Defining a Sequence Graph
The basic steps for defining a sequence graph are the same as those for
defining a function graph. Differences are noted below.
Setting Sequence Graph Modes
Press
z
to display the
MODE
settings. To graph sequence functions, you
must select
Seq
before you enter
WINDOW
variables or enter the sequence
functions. You may also want to select
Dot
to show discrete values more
clearly. Note that sequence graphs automatically plot in
Simul
MODE
,
regardless of the current
MODE
setting.
Displaying Sequence Functions
After selecting
Seq
MODE
, press
o
to display the sequence
Y=
edit screen.
On this screen, you display and enter the sequence functions,
U
n
and
V
n
.
Defining Sequence Functions
Follow the same procedures as for
Func
graphing to enter the expression
that defines a new sequence function. The
nth
term of
U
n
or
V
n
may be
defined in one of two ways:
¦
Explicitly in terms of
n
; for example,
U
n
=1
à
2^
n
. (
n
is the
2nd
function
of
®
on the keyboard, you cannot use
„
.)
¦
Recursively in terms of the prior element in a sequence using the
variables
U
n
-
1
and
V
n
-
1
(the
2nd
functions of
¬
and
−
); for example,
U
n
=1
à
2^
n
can be entered as
U
n
=(1
à
2)U
n
-
1
for
U
n
Start=1
.
6-4 Sequence Graphing
8206SEQ.DOC TI-82, Chapter 6, English Bob Fedorisko Revised: 02/09/01 12:49 PM Printed: 02/09/01
12:50 PM Page 4 of 6
Selecting Sequence Functions
Only the selected sequence functions are graphed. On selected functions
the
=
sign is highlighted. You may select one or both of the functions on the
sequence
Y=
edit screen.
To change the selection status of a sequence function, press
|
to move the
cursor onto the
=
sign and press
Í
.
Note: When you enter or edit either function, that function is selected
automatically.
Setting the WINDOW Variables
Press
p
to display the current
WINDOW
variable values. The
WINDOW
variables define the viewing
WINDOW
. The values shown are the
standard defaults.
UnStart=0
Value of
U
n
when
n
=
n
Start
VnStart=0
Value of
V
n
when
n
=
n
Start
nStart=0
Value of
n
at which calculation begins
nMin=0
Value of
n
at which plotting begins
nMax=10
Value of
n
at which plotting ends
Xmin=-10
Smallest
X
value to be displayed
Xmax=10
Largest
X
value to be displayed
Xscl=1
Spacing between
X
tick marks
Ymin=-10
Smallest
Y
value to be displayed
Ymax=10
Largest
Y
value to be displayed
Yscl=1
Spacing between
Y
tick marks
Note: If
U
n
or
V
n
is nonrecursive (not defined in terms of
U
n
-
1
or
V
n
-
1
),
then
n
Min
should not be
0
in
Time
FORMAT
.
n
Min
should usually equal
n
Start
+1 to obtain a meaningful graph.
Sequence Graphing 6-5
8206SEQ.DOC TI-82, Chapter 6, English Bob Fedorisko Revised: 02/09/01 12:49 PM Printed: 02/09/01
12:50 PM Page 5 of 6
Setting WINDOW FORMAT
Press
p
~
to display the current
WINDOW FORMAT
settings.
Sequence graphing has one unique format,
Time
or
Web
. The other formats
are shared with the other graphing modes.
PolarGC
is ignored in
Time
FORMAT
.
WINDOW FORMAT
Time Web
Sets type of sequence plot
RectGC PolarGC
Sets rectangular or polar cursor
CoordOn CoordOff
Sets cursor coordinate on or off
GridOff GridOn
Sets grid off or on
AxesOn AxesOff
Sets axes on or off
LabelOff LabelOn
Sets axes label off or on
Displaying a Graph
As a
Seq
graph is plotted, the TI
.
82 updates
X
,
Y
, and
n
. Smart Graph
applies to sequence graphs.
Time
plots the sequence as a function of
n
. It evaluates
U
n
and
V
n
for each
value of
n
(from
n
Min
to
n
Max
by
1
) and plots each point.
Web
calculates
U
n
as a function of
U
n
-
1
and
V
n
as a function of
V
n
-
1
. It
plots
U
n
-
1
and
V
n
-
1
(independent variables) on the horizontal axis and
U
n
and
V
n
(dependent variables) on the vertical axis. The line
Y=X
is plotted
automatically.
Evaluating U
n
and V
n
From the
Y
.
VARS
menu, you can access the function names
U
n
and
V
n
to:
¦
Calculate the
n
th value in a sequence.
¦
Calculate a list of values in a sequence.
¦
Generate a sequence with
U
n
(
nstart
,
nstop
,
nstep
)
.
nstep
is optional (if
not specified,
nstep
=1). Note:
U
n
and
V
n
are invalid with
seq(
.
6-6 Sequence Graphing
8206SEQ.DOC TI-82, Chapter 6, English Bob Fedorisko Revised: 02/09/01 12:49 PM Printed: 02/09/01
12:50 PM Page 6 of 6
Exploring a Sequence Graph
As in Function graphing, three tools are available for exploring a graph: using the
free-moving cursor, tracing a function, and zooming.
Free-Moving Cursor
The free-moving cursor works in
Seq
graphing just as it does in
Func
graphing. In
RectGC
FORMAT
, moving the cursor updates and displays (if
FORMAT
is
CoordOn
) the values of
X
and
Y
. (In
PolarGC Web
FORMAT
,
X
,
Y
,
R
, and
q
are updated, and
R
and
q
are displayed.)
TRACE
In
Time
FORMAT
, when you begin a trace, the cursor is on the first selected
function at
n
Min
.
TRACE
displays (if
FORMAT
is
CoordOn
) the values of
U
n
or
V
n
and
n
.
~
moves the cursor forward along the function one
n
at a
time. It updates
U
n
,
n
,
X
, and
Y
.
In
Web
FORMAT
, the trail left by the
TRACE
cursor helps identify points
with attracting and repelling behavior in the sequence. When you begin a
trace, the cursor is on the
X
axis at the value of
U
n
start
or
V
n
start
(the first
selected function).
TRACE
displays and updates (if
FORMAT
is
CoordOn
)
the values of
n
,
X
, and
Y
(or
R
and
q
).
X
and
Y
(or
R
and
q
) are calculated
from
n
.
~
moves the cursor between the function and the graph of
Y=X
,
displaying both for
n
before incrementing
n
.
If the cursor moves off the top or bottom of the screen, the coordinate
values at the bottom of the screen continue to change appropriately.
In
Seq
,
|
or
y
|
moves the
TRACE
cursor to
n
=
n
Min
.
QuickZoom and panning are available in
Seq
graphing.
ZOOM
ZOOM
operations works in
Seq
graphing as they do in
Func
graphing. Only
the
X
(
Xmin
,
Xmax
, and
Xscl
) and
Y
(
Ymin
,
Ymax
, and
Yscl
)
WINDOW
variables are affected.
U
n
start
,
V
n
start
,
n
Start
,
n
Min
, and
n
Max
are not
affected, except when you select
ZStandard
(
U
n
Start=0
,
V
n
Start=0
,
n
Start=0
,
n
Min=0
and
n
Max=10
). The
ZOOM MEMORY
variables in
Seq
graphing include
ZU
n
Start
,
ZV
n
Start
,
Z
n
Start
,
Z
n
Min
, and
Z
n
Max
.
CALC
value
is the only
CALC
operation available in
Seq
graphing. It is not
available in
Web
FORMAT
.
Tables 7-1
8207TABL.DOC TI-82, Chapter 7, English Bob Fedorisko Revised: 02/09/01 9:12 AM Printed: 02/09/01
12:37 PM Page 1 of 6
Chapter 7: Tables
This chapter describes how to use tables on the TI
.
82.
Chapter Contents
Getting Started: Roots of a Function
...............
7
-
2
Defining the Variables
.........................
7
-
3
Defining the Dependent Variable
.................
7
-
4
Displaying the Table
..........................
7
-
5
7-2 Tables
8207TABL.DOC TI-82, Chapter 7, English Bob Fedorisko Revised: 02/09/01 9:12 AM Printed: 02/09/01
12:37 PM Page 2 of 6
Getting Started: Roots of a Function
Getting Started is a fast-paced introduction. Read the chapter for details.
Evaluate the function Y=X
3
N
2X at each integer between
M
10 and 10. How many
sign changes are there and where do they occur?
1. Press
y
ã
TblSet
ä
to display the
TABLE SETUP
screen. Press
Ì
10
to set
TblMin=
M
10
. Leave
@
Tbl=1
. Leave the independent and dependent
value settings on
Auto
.
2. Press
o
„
3
(to select
3
)
¹
2
„
to
enter the function
Y
1
=X
3
–2X
.
3. Press
y
ã
TABLE
ä
to display the table screen.
4. Press
†
until you see the sign changes in the
value of
Y
1
.
Tables 7-3
8207TABL.DOC TI-82, Chapter 7, English Bob Fedorisko Revised: 02/09/01 9:12 AM Printed: 02/09/01
12:37 PM Page 3 of 6
Defining the Variables
The independent variable for tables is the independent variable in the current
graphing MODE. It is defined on the TABLE SETUP screen.
TABLE SETUP Screen
To display the
TABLE SETUP
screen, press
y
ã
TblSet
ä
.
TblMin and
@
Tbl
TblMin
(table minimum) applies when
Indpnt
is
Auto
(when the
independent variable is automatically generated). It defines the initial value
for the independent variable:
X
(
Func
),
T
(
Par
),
q
(
Pol
), and
n
(
Seq
).
@
Tbl
(table step) defines the increment for the independent variable.
Note: In
Seq
MODE
,
TblMin
and
@
Tbl
both must be integers.
Indpnt: Auto or Ask
You can choose to display a table of values for the independent variable
automatically or enter the values one at a time on the table.
Auto
generates
and displays the values when the table is first displayed.
Ask
displays an
empty table and you enter the values.
Depend: Auto or Ask
You can choose to display the values for the dependent variables
automatically or one at a time.
Auto
calculates and displays all table values
when the table is first displayed.
Ask
displays a table without values for the
dependent variables. It calculates and displays a value for a specific
location when you press
Í
.
Setting Up a Table from the Home Screen or a Program
You can store values to
TblMin
,
@
Tbl
, and
Tbl
Z
nput
from the Home screen
or a program. The variable names are on the
VARS TABLE
menu.
Tbl
Z
nput
is a list of the values of the independent variable in the current table. In the
program editor, when you press
y
[
TblSet
], you can select instructions for
IndpntAuto
,
IndpntAsk
,
DependAuto
, or
DependAsk
.
7-4 Tables
8207TABL.DOC TI-82, Chapter 7, English Bob Fedorisko Revised: 02/09/01 9:12 AM Printed: 02/09/01
12:37 PM Page 4 of 6
Defining the Dependent Variable
The selected Y
n
functions define the dependent variables. You can have as many
dependent variables as there are functions in the current graphing MODE.
From the Y= Editor
Enter the functions to define the dependent variables in the
Y=
editor. The
current graphing
MODE
is used. In
Par
, you must define both components
of the parametric equation. Only functions that are selected are displayed
in the table (Chapter 3).
From the Table Editor
Once a
Y=
function has been entered and selected, you can change it from
the table editor.
1. Move the cursor to the column of the dependent variable.
2. Press
}
until the cursor is on the name of the function at the top of the
column. The function is displayed on the bottom line.
3. You may edit the function. Press
Í
to switch to the editing context
and make the changes. The function in the
Y=
table is updated.
4. Press
Í
or
†
. The new values are calculated, and the table is
updated automatically.
Note: This feature also allows you to view the function that defines the
dependent variable(s) without leaving the table.
Tables 7-5
8207TABL.DOC TI-82, Chapter 7, English Bob Fedorisko Revised: 02/09/01 9:12 AM Printed: 02/09/01
12:37 PM Page 5 of 6
Displaying the Table
The table displays two independent values for up to seven dependent values.
Once the table is displayed, you can use
|
,
}
,
~
, and
†
to move around and
scroll the table, displaying other independent variables and other dependent
values.
The Table
Press
y
ã
TABLE
ä
to display the table screen.
The top line displays the name of the independent variable and one or two
dependent variables. The bottom line displays the full value of the current
cell, as indicated by the rectangular cursor. The center portion is used to
display the values, abbreviated if necessary, of the variables.
The selections you made on the
TABLE SETUP
screen determine which
cells contain values when you press
y
ã
TABLE
ä
.
Indpnt: Auto
Depend: Auto
Values appear in all cells in the table automatically.
Indpnt: Ask
Depend: Auto
Table is empty. When a value is entered for the
independent variable, the dependent values are
calculated automatically.
Indpnt: Auto
Depend: Ask
Values appear for the independent variable. To
generate a value for a dependent variable, move to the
specific cell and press
Í
.
Indpnt: Ask
Depend: Ask
Table is empty. Enter values for independent variable.
To generate a value for a dependent variable, move to
the specific cell and press
Í
.
7-6 Tables
8207TABL.DOC TI-82, Chapter 7, English Bob Fedorisko Revised: 02/09/01 9:12 AM Printed: 02/09/01
12:37 PM Page 6 of 6
Displaying More Independent Values
If you selected
Indpnt: Auto
, you can use
}
and
†
to display additional
values of the independent variable and the corresponding dependent
variables.
Note:
You can scroll “back” from the value entered for
TblMin
. As you
scroll,
TblMin
is updated automatically to the value shown on the top line
of the table. For example,
TblMin=0
and
@
Tbl=1
generates and displays
values of
X
=0, . . ., 6, but you can press
}
to scroll backwards and display
the table for
X
=
L
1, . . ., 5.
Displaying Other Dependent Variables
If you have more than two dependent variables defined, the first two in the
Y=
list are displayed. Press
~
and
|
to display other dependent variables.
Clearing the Table
From a program, select the
ClrTable
instruction from the
PRGM I/O
menu.
If
TblSet
is
IndpntAsk
, all independent variable values and dependent
variable values on the table are cleared. If
TblSet
is
DependAsk
, all
dependent variable values on the table are cleared.
DRAW
Operations 8-1
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 1 of 16
Chapter 8: DRAW Operations
This chapter describes how to use the DRAW operations of the TI
.
82. Before
using the DRAW operations, you should be familiar with Chapter 3, Function
Graphing.
Chapter Contents
Getting Started: Shading a Graph
.................
8-2
DRAW DRAW
Menu
...........................
8-3
Drawing Lines
...............................
8-4
Drawing Horizontal and Vertical Lines
.............
8-5
Drawing Tangent Lines
........................
8-6
Drawing Functions and Inverses
.................
8-7
Shading Areas on a Graph
......................
8-8
Drawing Circles
.............................
8-9
Placing Text on a Graph
.......................
8-10
Using
Pen
to Draw on a Graph
...................
8-11
Drawing Points
..............................
8-12
Drawing Pixels
..............................
8-13
Storing and Recalling Graph Pictures
..............
8-14
Storing and Recalling Graph Databases
.............
8-15
Clearing a Drawing
...........................
8-16
8-2
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 2 of 16
Getting Started: Shading a Graph
Getting Started is a fast-paced introduction. Read the chapter for details.
Shade the area above the function Y=X+1 and below the function Y=X
3
–8X.
1. Press
o
to see that all functions are deselected.
2. Press
q
6
to reset the graph screen to the
standard viewing
WINDOW
, clear any existing
drawings, and display the viewing window.
3. Press
y
ã
DRAW
ä
and press
7
to select
Shade(
,
which is copied to the Home screen.
4. Press
„
Ã
1
¢
to define the function above
which you want to shade.
5. Press
„
3
(to select
3
)
¹
8
„
¢
to
define the function below which you want to
shade.
6. Press
2
¤
to define the resolution for shading
the graph.
7. Press
Í
to execute the instruction. The two
functions are drawn and the specified area
shaded.
DRAW
Operations 8-3
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 3 of 16
DRAW DRAW Menu
To display the DRAW DRAW menu, press
y
<
. What happens when you
select an item from this menu is dependent on whether or not a graph is
displayed when you access the menu, as described under each operation.
DRAW DRAW Menu
DRAW POINTS STO
1: ClrDraw
Clears all drawn elements.
2: Line(
Draws a line between two points.
3: Horizontal
Draws a horizontal line.
4: Vertical
Draws a vertical line.
5: Tangent(
Draws a line tangent to a function.
6: DrawF
Draws a function.
7: Shade(
Shades an area.
8: DrawInv
Draws the inverse of a function.
9: Circle(
Draws a circle.
0: Text(
Annotates a graph with text.
A: Pen
Free-form drawing tool.
See page 8
.
16 for
ClrDraw
.
Before Drawing on a Graph
Because
DRAW
operations draw on top of the graph of currently selected
functions, you may want to do one or more of the following before drawing
on a graph:
¦
Change the
MODE
settings.
¦
Change the
WINDOW FORMAT
settings.
¦
Enter or edit functions in the
Y=
list.
¦
Select or deselect functions in the
Y=
list.
¦
Change
WINDOW
variable values.
¦
Turn
Stat Plots
on or off.
¦
Clear existing drawings with
ClrDraw
(page 8
.
16).
Drawing on a Graph
DRAW
operations can draw on
Func
,
Par
,
Pol
, and
Seq
graphs, except
DrawInv
, which is valid only in
Func
graphing. The coordinates for all
DRAW
instructions are always the
X
-coordinate and
Y
-coordinate values of
the display.
You can use most of the
DRAW DRAW
and
DRAW POINTS
operations to
draw directly on a graph using the cursor to identify coordinates, or you
can execute these instructions from the Home screen or a program. If a
graph is not displayed when you select a
DRAW
operation, the Home
screen is displayed automatically.
8-4
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 4 of 16
Drawing Lines
While a graph is displayed, Line( lets you define a line on the graph using the
cursor. If a graph is not displayed, the instruction is copied to the Home screen.
Directly on a Graph
1. When a graph is displayed, select
Line(
from the
DRAW DRAW
menu
(item
2
).
2. Position the cursor at the beginning point of the line you want to draw.
Press
Í
.
3. Move the cursor to the end point of the line you want to draw. The line
is displayed as you move the cursor. Press
Í
.
To continue to draw lines, repeat steps 2 and 3. To cancel
Line(
, press
‘
.
From the Home Screen or a Program
Line(
(
DRAW DRAW
item
2
) draws a line between the coordinates (
X1
,
Y1
)
and (
X2
,
Y2
). The values may be entered as expressions.
Line(
X1
,
Y1
,
X2
,
Y2
)
For example,
Line(0,0,6,9)
displays:
To erase a line:
Line(
X1
,
Y1
,
X2
,
Y2
,0)
For example,
Line(2,3,4,6,0)
following the instruction above displays:
DRAW
Operations 8-5
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 5 of 16
Drawing Horizontal and Vertical Lines
While a graph is displayed, Horizontal and Vertical let you define lines on the
graph using the cursor. If a graph is not displayed, the instruction is copied to the
Home screen.
Directly on a Graph
1. When a graph is displayed, select
Horizontal
(item
3
) or
Vertical
(item
4
) from the
DRAW DRAW
menu.
2. A line is displayed that moves as you move the cursor. Position the
cursor where you want to draw the line. Press
Í
. The line is drawn
on the graph.
To continue to draw lines, repeat step 2. To cancel
Horizontal
or
Vertical
,
press
‘
.
From the Home Screen or a Program
Horizontal
(horizontal line) (
DRAW DRAW
item
3
) draws a horizontal line
at
Y
=
Y
(which can be an expression, but not a list).
Horizontal
Y
Vertical
(vertical line) (
DRAW DRAW
item
4
) draws a vertical line at
X
=
X
(which can be an expression, but not a list).
Vertical
X
For example,
Horizontal 7:Vertical 4:Vertical 5
displays:
8-6
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 6 of 16
Drawing Tangent Lines
While a graph is displayed, you can draw the tangent line of a function at a
specified point using the cursor. If a graph is not displayed, the instruction is
copied to the Home screen.
Directly on a Graph
1. When a graph of selected functions is displayed, select
Tangent(
from
the
DRAW DRAW
menu (item
5
).
2. Use
†
and
}
to move the cursor to the function for which you want to
draw the tangent line.
3. Use
~
and
|
to move the cursor to the point on the function at which
you want to draw the tangent line.
4. Press
Í
.
From the Home Screen or a Program
Tangent(
(tangent line) (
DRAW DRAW
item
5
) draws a line tangent to an
expression
in terms of
X
(such as
Y
1
or
X
2
) at point
X
=
value
(which can be
an expression).
expression
is interpreted as being in
Func
MODE
.
Tangent(
expression
,
value
)
For example, if
Y
1
=.2X
3
–2X+6
is the only selected function,
Tangent(Y
1
,3)
plots
Y
1
and draws the tangent to the function at
X
=3:
DRAW
Operations 8-7
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 7 of 16
Drawing Functions and Inverses
DrawF (draw function) draws a function on the current graph. DrawInv (draw
inverse) draws an inverse of a function on the current graph. Both instructions
must be entered on the Home screen or in the program editor.
Drawing a Function
DrawF
(draw function) (
DRAW DRAW
item
6
) is not an interactive
operation. It draws
expression
as a function in terms of
X
on the current
graph.
DrawF
expression
For example, if
Y
1
=.2X
3
–2X+6
is the only selected function,
DrawF Y
1
–5
plots
Y
1
and draws the function
Y
1
–5
:
Note: A list cannot be used in
expression
to draw a family of curves.
Drawing an Inverse of a Function
DrawInv
(draw inverse) (
DRAW DRAW
item
8
) is not an interactive
operation. It draws the inverse of an
expression
in terms of
X
on the
current graph. You must be in
Func
MODE
.
DrawInv
expression
For example, if
Y
1
=.2X
3
–2X+6
is the only selected function,
DrawInv Y
1
plots
Y
1
and draws its inverse:
8-8
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 8 of 16
Shading Areas on a Graph
Shade( shades the area on a graph that is both below one specified function and
above another, between two X values. The instruction must be entered on the
Home screen or in the program editor.
Shading a Graph
Shade(
(
DRAW DRAW
item
7
) is not an interactive operation. It draws
lowerfunc
and
upperfunc
in terms of
X
on the current graph and shades the
area that is specifically above
lowerfunc
and below
upperfunc
. Only the
areas where
lowerfunc
<
upperfunc
are shaded.
You can specify the shading
resolution
(an integer between 1 and 9). If
none is specified, 1 is used.
resolution
=1 shades every pixel.
resolution
=2
shades every second pixel.
resolution
=3 shades every third pixel, and so
on.
Optionally, you can specify
Xleft
(the left boundary) and
Xright
(the right
boundary) for the shaded area. If
Xleft
or
Xright
are not specified,
Xmin
and
Xmax
are used.
Shade(
lowerfunc
,
upperfunc
)
Shade(
lowerfunc
,
upperfunc
,
resolution
)
Shade(
lowerfunc
,
upperfunc
,
resolution
,
Xleft
)
Shade(
lowerfunc
,
upperfunc
,
resolution
,
Xleft
,
Xright
)
For example,
Shade(X
3
–8X,X–2):Shade(X–2,X
3
–8X,2,-2,5)
displays:
DRAW
Operations 8-9
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 9 of 16
Drawing Circles
While a graph is displayed, Circle( lets you define a circle on the graph using the
cursor. If a graph is not displayed, the instruction is copied to the Home screen.
Directly on a Graph
1. When a graph is displayed, select
Circle(
from the
DRAW DRAW
menu
(item
9
).
2. Position the cursor at the center of the circle you want to draw. Press
Í
.
3. Move the cursor to a point on the circumference. Press
Í
. The
circle is drawn on the graph.
To continue to draw circles, repeat steps 2 and 3. To cancel
Circle(
press
‘
.
Because this circle is drawn on the display and is independent of the
WINDOW
values (unlike the
Circle(
instruction, see below), it appears as a
circle.
From the Home Screen or a Program
Circle(
(
DRAW DRAW
item
9
) draws a circle with center (
X
,
Y
) and
radius
(these values can be expressions).
Circle(
X
,
Y
,
radius
)
Note: When the
Circle(
instruction is used from a program, the drawn
circle may not look like a circle because it is drawn with respect to the
current
WINDOW
values. For example, in the standard viewing
WINDOW
,
Circle(0,0,7)
displays:
8-10
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 10 of 16
Placing Text on a Graph
While a graph is displayed, Text( lets you place text on it. If a graph is not
displayed, the instruction Text( is copied to the Home screen.
Directly on a Graph
1. When a graph is displayed, select
Text(
from the
DRAW DRAW
menu.
2. Position the cursor where you want the text to begin.
3. Type the characters. You may enter TI
.
82 functions and instructions.
The font is proportional, so the exact number of characters you can
place is variable. As you type, the characters are placed on top of the
graph.
To cancel
Text(
, press
‘
.
From the Home Screen or a Program
Text(
(
DRAW DRAW
item 0) places the characters in
text
(which can
include TI
.
82 functions and instructions, except
!
) on the current graph.
The upper left of the first character is at pixel (
row
,
column
), where
row
is
an integer between 0 and 57 (which can be an expression) and
column
is an
integer between 0 and 94 (which can be an expression).
Text(
row
,
column
,
value
,
value
. . .
)
value
may be text enclosed in
"
marks or an expression, which will be
evaluated and the result displayed with up to 10 characters. For example, if
Y
1
=.2X
3
–2X+6
is the only selected function,
Text(42,52,"Y=.2X
3
–2X+6")
displays:
Split Screen
In
Split
screen
MODE
, the maximum value of
row
is 25.
DRAW
Operations 8-11
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 11 of 16
Using Pen to Draw on a Graph
While a graph is displayed, Pen lets you draw directly on the graph with the
cursor.
Using Pen
Pen
draws directly on a graph. It is not accessible from the Home screen or
a program.
1. When a graph is displayed, select
Pen
from the
DRAW DRAW
menu
(item
A
).
2. Position the cursor where you want to begin drawing. Press
Í
to
turn the pen on.
3. As you move the cursor, it draws on the graph, turning on each point
that the cursor crosses.
4. Press
Í
to turn the pen off. Move the cursor to a new position
where you want to begin drawing again.
To continue to draw on the graph with the pen, repeat steps 2, 3, and 4. To
cancel
Pen
, press
‘
.
For example,
Pen
was used to create the arrow pointing to the local
minimum of the selected function.
8-12
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 12 of 16
Drawing Points
To display the DRAW POINTS menu, press
y
<
~
. What happens when you
select an item from this menu is dependent on whether or not a graph is
displayed when you access the menu, as described under each operation.
DRAW POINTS Menu
DRAW POINTS STO
1: Pt-On(
Turn on a point.
2: Pt-Off(
Turn off a point.
3: Pt-Change(
Toggle a point on or off.
4: Pxl-On(
Turn on a pixel.
5: Pxl-Off(
Turn off a pixel.
6: Pxl-Change(
Toggle a pixel on or off.
7: pxl-Test(
Return 1 if pixel is on, 0 if off.
Directly on a Graph
1. When a graph is displayed, select
Pt
.
On(
from the
DRAW POINTS
menu.
2. Position the cursor at the location on the display where you want to
draw the point. Press
Í
. The point is drawn.
To continue to draw points, repeat step 2. To cancel
Pt
.
On(
, press
‘
.
Pt-Off(, Pt Change(
The procedure for using
Pt
.
Off(
(point off) to turn off (erase) a point and
Pt
.
Change(
(point change) to toggle (reverse) a point on and off is the
same as for
Pt
.
On
.
Pt
.
Off(
X
,
Y
)
Pt
.
Change(
X
,
Y
)
From the Home Screen or a Program
Pt
.
On(
(point on) turns on the point at (
X
=
X
,
Y
=
Y
).
Pt
.
On(
X
,
Y
)
DRAW
Operations 8-13
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 13 of 16
Drawing Pixels
The Pxl (pixel) operations let you turn on, turn off, or reverse a pixel (a dot) on the
graph using the cursor. The instruction must be entered on the Home screen or
in the program editor.
TI
.
82 Pixels
Turning Pixels On and Off
The pixel instructions are not interactive.
Pxl
.
On(
(pixel on)
(
DRAW POINTS
item
9
) turns on the pixel at (
row
,
column
), where
row
is
an integer between 0 and 62 and
column
is an integer between 0 and 94.
Pxl
.
On(
row
,
column
)
Pxl
.
Off(
row
,
column
)
Pxl
.
Change(
row
,
column
)
pxl-Test(
pxl
.
Test(
(pixel test) (
DRAW POINTS
item
7
) returns 1 if a pixel
(
row
,
column
) is
On
or 0 if it is
Off
on the current graph.
row
must be an
integer between 0 and 62.
column
must be an integer between 0 and 94.
pxl
.
Test(
row
,
column
)
Split Screen
In
Split
screen
MODE
, the maximum value of
row
is 30 in
Pxl
.
On(
,
Pxl
.
Off(
,
Pxl
.
Change(
, and
pxl
.
Test(
.
8-14
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 14 of 16
Storing and Recalling Graph Pictures
Press
y
<
|
to display the DRAW STO menu. You can store an image of the
current display and superimpose that image onto a displayed graph at a later
time from the Home screen or a program.
DRAW STO Menu
DRAW POINTS STO
1: StorePic
Store the current picture.
2: RecallPic
Recall a saved picture.
3: StoreGDB
Store the current graph database.
4: RecallGDB
Recall a saved graph database.
Storing a Graph Picture
A picture includes drawn elements, plotted functions, axes, and tick marks.
The picture does not include axis labels, lower and upper bound indicators,
prompts, or cursor coordinates. Any parts of the display “hidden” by these
are stored with the picture.
1. Press
y
ã
DRAW
ä
|
(to display the
DRAW STO
menu)
1
(to select
StorePic
).
StorePic
is copied to the Home screen or program editor.
2. Press
4
(to display the
VARS PIC
menu). Select
Pic1
,
Pic2
,
Pic3
,
Pic4
,
Pic5
, or
Pic6
.
StorePic Pic
n
3. Press
Í
. The current graph is displayed and the picture is stored.
Recalling a Graph Picture
1. Press
y
ã
DRAW
ä
|
(to display the
DRAW STO
menu)
2
(to select
RecallPic
).
RecallPic
is copied to the Home screen or program editor.
2. Press
4
(to display the
VARS PIC
menu). Select
Pic1
,
Pic2
,
Pic3
,
Pic4
,
Pic5
, or
Pic6
.
RecallPic Pic
n
3. Press
Í
. The current graph is displayed if necessary, and the
picture is superimposed.
Note: Pictures are drawings. You cannot
TRACE
any curve on a picture.
Deleting a Graph Picture
Graph pictures are deleted from memory through the
MEM
menu (Chapter
15.)
DRAW
Operations 8-15
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 15 of 16
Storing and Recalling Graph Databases
A graph database is the set of elements that define a particular graph. The graph
can be recreated from these elements. You can store up to six graph databases
and recall any of them to recreate a graph at a later time.
Graph Databases
The elements of a graph database are:
¦
Graphing
MODE
.
¦
WINDOW
variables and
WINDOW FORMAT.
¦
All functions in the
Y=
list, and whether they are selected.
Graph databases do not include any drawn items or any
Stat Plot
definitions.
Storing a Graph Database
1. Press
y
ã
DRAW
ä
|
(to display the
DRAW STO
menu)
3
(to select
StoreGDB
).
StoreGDB
is copied to the Home screen or program editor.
2. Press
3
(to display the
VARS GDB
menu). Select
GDB1
,
GDB2
,
GDB3
,
GDB4
,
GDB5
, or
GDB6
.
3. Press
Í
. The current database is stored.
StoreGDB GDB
n
Recalling a Graph Database
Caution: When you recall a graph database, all existing
Y=
functions are
replaced. You may want to store the current
Y=
functions to another
database before recalling a stored database.
1. Press
y
ã
DRAW
ä
|
(to display the
DRAW STO
menu)
4
(to select
RecallGDB
).
RecallGDB
is copied to the Home screen or program
editor.
2. Press
3
(to display the
VARS GDB
menu). Select
GDB1
,
GDB2
,
GDB3
,
GDB4
,
GDB5
, or
GDB6
.
RecallGDB GDB
n
3. Press
Í
. The new graph database replaces the current one. The
new graph is not plotted. (The TI
.
82 changes graphing
MODE
automatically, if necessary.)
Deleting a Graph Database
Graph databases are deleted from memory through the
MEM
menu
(Chapter 15.)
8-16
DRAW
Operations
8208DRAW.DOC TI-82, Chapter 8, English Bob Fedorisko Revised: 02/09/01 12:23 PM Printed:
02/09/01 3:30 PM Page 16 of 16
Clearing a Drawing
All points, lines, and shading drawn on a graph with DRAW operations are
temporary. They remain only until you execute a ClrDraw (clear drawing)
instruction or a change prompts Smart Graph to replot the graph, at which time
all drawn elements are erased.
When a Graph is Displayed
To clear drawings from the currently displayed graph, select
ClrDraw
from
the
DRAW DRAW
menu (item
1
). The current graph is plotted and displayed
immediately with no drawn elements.
From the Home Screen or a Program
Begin on a blank line on the Home screen or in the program editor. Select
ClrDraw
from the
DRAW DRAW
menu (item
1
). The instruction is copied to
the cursor location.
When the instruction is executed, it clears all drawings from the current
graph and displays the message
Done
. The next time you display the graph,
all drawn points, lines, circles, and shaded areas will be gone.
Note: Before you clear drawings, you can store them with
StorePic
(page
8
.
14).
Split Screen 9-1
8209SPLT.DOC TI-82, Chapter 9, English Bob Fedorisko Revised: 02/09/01 9:16 AM Printed: 02/09/01
12:37 PM Page 1 of 4
Chapter 9: Split Screen
On the TI
.
82, you can simultaneously display a graph (including a stat plot) and
an editor such as the Home screen, Y= editor, list editor, or table editor.
Chapter Contents
Getting Started: Polynomial Coefficients
............
9-2
Using Split Screen
............................
9-3
9-2 Split Screen
8209SPLT.DOC TI-82, Chapter 9, English Bob Fedorisko Revised: 02/09/01 9:16 AM Printed: 02/09/01
12:37 PM Page 2 of 4
Getting Started: Polynomial Coefficients
Getting Started is a fast-paced introduction. Read the chapter for details.
Use the split screen capability to explore the behavior of the graph of a
polynomial as the coefficients change.
1. In
Func
MODE
, press
o
to display the
Y=
screen. Press
.1
„
3
(to select
3
)
¹
2
„
Ã
6
Í
to enter the polynomial
.1X
3
N
2X+6
.
2. Press
z
to enter display the
MODE
screen.
Press
†
†
†
†
†
†
~
Í
to set the
screen to
Split
.
3. Press
q
6
(to select
ZStandard
). The TI
.
82
split screen is displayed. The current graph is
plotted in the standard viewing
WINDOW
(just
compressed) and displayed on the top half of
the display. The bottom half is blank.
4. Press
~
to activate the free-moving cursor.
5. Press
o
. The
Y=
editor displays on the bottom
half of the display and the cursor moves to the
Y=
editor.
6. Press
~
to move the cursor over the 1. Press
5
.
The graph does not change.
7. Press
s
to plot the new graph. This also
moves the cursor to the upper window. Press
~
to see the free-moving cursor.
Split Screen 9-3
8209SPLT.DOC TI-82, Chapter 9, English Bob Fedorisko Revised: 02/09/01 9:16 AM Printed: 02/09/01
12:37 PM Page 3 of 4
Using Split Screen
Once you have selected split screen, it remains in effect until you change it. A
split-screen display may be replaced temporarily by a full-screen display. When
you press a key in split-screen MODE, the cursor automatically moves to the
correct half of the display for that key.
Setting Screen MODE
To change the screen
MODE
from
FullScreen
to
Split
or vice versa, you
must use the
MODE
screen.
Split Screen: Top
The top half displays the graph screen (any
MODE
).
The cursor is placed in the upper half of the display by
GRAPH
,
TRACE
, a
ZOOM
operation, or a
CALC
operation.
Split Screen: Bottom
The bottom half displays an editor.
¦
Home screen (4 lines)
¦
Y=
editor (4 lines)
¦
Table (2 rows)
¦
STAT
list editor (2 rows)
¦
WINDOW
(3 settings, can be scrolled)
The cursor is placed in the bottom half of the display whenever a key is
pressed that moves to one of these displays.
Exceptions
The split screen will be replaced temporarily by a full-screen display for:
¦
Full-screen menus
¦
MODE
screen,
WINDOW FORMAT
screen
¦
Matrix editor
¦
TABLE SETUP
,
SET UP CALCS
,
STAT PLOTS
¦
Program editor
¦
Memory management
9-4 Split Screen
8209SPLT.DOC TI-82, Chapter 9, English Bob Fedorisko Revised: 02/09/01 9:16 AM Printed: 02/09/01
12:37 PM Page 4 of 4
TI-82 Pixels
DRAW Pixels Instructions
The maximum value of
row
is 30 in the
Pxl-On(
,
Pxl-Off(
,and
Pxl-Change(
instructions and the
pxl-Test(
function when
MODE
is
Split
.
Pxl-On(
row
,
column
)
DRAW Text Instruction
The maximum value of
row
is 25 in the
Text(
instruction when
MODE
is
Split
.
Text(
row
,
column
,"
text
")
PRGM Output Instruction
The maximum value of
row
is 4 in the
Output(
instruction when
MODE
is
Split
.
Output(
row
,
column
,"
text
")
Setting Screen MODE from the Home Screen or a Program
To set screen
MODE
from a program, press
z
on a blank line in the
program editor and select
FullScreen
or
Split
. The instruction is copied to
the cursor location. The
MODE
is set when the instruction is encountered
during execution and remains in effect after the program is done.
Matrices 10-1
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 1 of 14
Chapter 10: Matrices
This chapter describes the matrix features of the TI
.
82. The TI
.
82 can store up to
five matrices. A matrix, depending on available memory, may have up to 99 rows
or columns.
Chapter Contents
Getting Started: Systems of Linear Equations
........
10-2
Defining a Matrix
............................
10-4
Viewing Matrix Elements
.......................
10-5
Editing Matrix Elements
.......................
10-6
About Matrices
..............................
10-8
Matrix Math Functions
........................
10-10
MATRIX MATH
Operations
......................
10-12
10-2 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 2 of 14
Getting Started: Systems of Linear Equations
Getting Started is a fast-paced introduction. Read the chapter for details.
Find the solution of x + 2y + 3z = 3 and 2x + 3y + 4z = 3. On the TI
.
82, you can
solve a system of linear equations by entering the coefficients as elements in a
matrix and then using the matrix row operations to obtain the reduced row
echelon form.
1. Press
. Press
~
~
to display the
MATRX EDIT
menu. Press
1
to select
ã
A
ä
to edit
matrix
ã
A
ä
.
2. Press
2
Í
4
Í
to define a 2×4 matrix.
The rectangular cursor indicates the current
element. The ellipses points at the right
indicate that one or more additional columns
exist.
3. Press
1
Í
to enter the first element. The
rectangular cursor moves to the second
column of the first row.
4. Press
2
Í
3
Í
3
Í
to complete the
top row.
5. Press
2
Í
3
Í
4
Í
3
Í
to enter
the bottom row.
Matrices 10-3
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 3 of 14
6. Press
y
ã
QUIT
ä
to return to the Home screen.
Begin on a blank line. Press
~
to
display the
MATRX MATH
menu. Press
†
until
the bottom items on the menu are shown, then
select
…
row+(
(item
A
).
…
row+(
is copied to the
Home screen.
7. Press
Ì
2
¢
. Press
1
(to select
ã
A
ä
from the
MATRX NAMES
menu). Press
¢
1
¢
2
¤
Í
. This multiplies row 1 by
L
2 and
adds it to row 2. The resulting matrix is
displayed and stored in
Ans
. The value of
ã
A
ä
is
not changed.
8. Press
~
to display the
MATRX MATH
menu. Select
…
row(
(item
0
) and then press
Ì
1
¢
y
ã
Ans
ä
¢
2
¤
Í
. This multiplies row
2 of the matrix in
Ans
by
L
1. Again, the
resulting matrix is displayed and stored in
Ans
.
9. Press
~
. Select
…
row+(
(item
A
). Press
Ì
2
¢
y
ã
Ans
ä
¢
2
¢
1
¤
Í
. This
multiplies row 2 of the matrix in
Ans
by
L
2 and
adds it to row 1. The resulting reduced row-
echelon form of the matrix is displayed and
stored in
Ans
.
1x
N
1z =
L
3sox=
-
3+ z
1y + 2z = 3 y = 3
N
2z
10-4 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 4 of 14
Defining a Matrix
A matrix is a two-dimensional array. You can display, enter, or edit a matrix in the
matrix editor. The TI
.
82 has five matrix variables:
ã
A
ä
,
ã
B
ä
,
ã
C
ä
,
ã
D
ä
, or
ã
E
ä
. You can
define a matrix directly in an expression.
Selecting a Matrix
To define or display a matrix in the editor, you first must select the name of
the matrix.
1. Press
~
~
to display the
MATRX EDIT
menu.
2. Select the matrix you want to define (either
ã
A
ä
,
ã
B
ä
,
ã
C
ä
,
ã
D
ä
, or
ã
E
ä
). The
MATRX EDIT
screen appears.
Accepting or Changing Matrix Dimensions
The dimensions of the matrix (row × column) are displayed on the top line.
When you select a matrix to define, the cursor is on the row dimension.
You must accept or change the dimensions each time you enter or edit a
matrix. A “new” matrix has dimension 1×1.
1. Accept or change the number of rows.
¦
To accept the number, press
Í
.
¦
To change the number, enter the number of rows (up to 99), and then
press
Í
.
The cursor moves to the number of columns.
2. Accept or change the number of columns as above.
The rectangular cursor moves to the first matrix element.
Matrices 10-5
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 5 of 14
Viewing Matrix Elements
After the dimensions of the matrix are set, the matrix can be viewed and values
can be entered into the matrix elements. In a “new” matrix, all values are zero.
Displaying Matrix Elements
The center portion of the matrix editor displays up to seven rows and three
columns of a matrix, showing the values of the elements in abbreviated
form if necessary. The full value of the current element (indicated by the
rectangular cursor) is shown on the bottom line.
An 8×4 matrix is shown. The ellipses marks and
$
in the right column
indicate additional rows and columns.
Leaving the MATRX Edit Screen
To leave the
MATRX
edit screen:
¦
Select another screen by pressing the appropriate key.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
Deleting a Matrix
Matrices are deleted from memory through the
MEM
menu (Chapter 15).
10-6 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 6 of 14
Editing Matrix Elements
The matrix editor has two “contexts,” viewing and editing. The current context
determines the result of a keystroke.
Viewing a Matrix
In viewing context, you can move quickly from one matrix element to the
next. The full value of the current element is displayed on the bottom line.
Viewing Context Keys
|
or
~
Moves the rectangular cursor within the current row.
†
or
}
Moves the rectangular cursor within the current
column. On the top row,
}
moves cursor to the column
dimension. On the column dimension, moves cursor to
the row dimension.
Í
Switches to editing context; activates the edit cursor on
the bottom line.
‘
Switches to editing context; clears the value on the
bottom line.
A
ny entry
character
Switches to editing context; clears the value on the
bottom line; copies the character to the bottom line.
y
[
INS
] Nothing.
{
Nothing.
Matrices 10-7
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 7 of 14
Editing a Matrix Element
In editing context, an edit cursor is active on the bottom line, and you can
change the value of the current matrix element.
1. Use the cursor-movement keys to move the cursor to the matrix
element you want to change.
2. Switch to editing context by pressing
Í
,
‘
, or an entry key.
3. Change the value of the matrix element. You may enter an expression
(which is evaluated when you leave the editing context) for the value.
Note: You can press
‘
, followed by
Í
to restore the value at
the rectangular cursor if you make a mistake.
4. Press
Í
,
}
, or
†
to move to another element.
Editing Context Keys
|
or
~
Moves the edit cursor within the value.
†
or
}
Stores the value on the bottom line to the matrix
element; switches to viewing context and moves the
rectangular cursor within the column.
Í
Stores the value on the bottom line to the matrix
element; switches to viewing context. Rectangular
cursor moves to the next element.
‘
Clears the value on the bottom line.
A
ny entry
character
Copies the character to the location of the edit cursor
on the bottom line.
y
[
INS
] Activates insert cursor.
{
Deletes the character under the edit cursor on the
bottom line.
10-8 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 8 of 14
About Matrices
On the Home screen or in a program, you can use, enter, store, and display
matrices.
Using a Matrix in an Expression
To use a matrix in an expression, you may:
¦
Copy the name from the
MATRIX NAMES
menu.
¦
Recall the contents of the matrix into the expression with
y
[
RCL
]
(Chapter 1).
¦
Enter the matrix directly (see below).
Entering a Matrix in an Expression
You can enter, edit, and store a matrix in the
MATRIX
editor. You also can
enter a matrix directly in an expression.
1. Press
y
ã
ã
ä
to indicate the beginning of the matrix.
2. Press
y
ã
ã
ä
to indicate the beginning of a row.
3. Enter a value (which can be an expression) for each element in the row,
separated by commas.
4. Press
y
ã
ä
ä
to indicate the end of a row.
5. Repeat steps 2 through 4 to enter all of the rows.
6. Press
y
ã
ä
ä
to indicate the end of the matrix.
Note: The closing
]]
is not necessary at the end of an expression or
preceding
!
.
[[
element
1,1
,
. . .
,
element
1,n
]
. . .
[
element
m
,
. . .
,
element
m,n
]]
The expression is evaluated when the entry is executed. Commas are required
on entry to separate elements, but are not displayed on output.
Matrices 10-9
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 9 of 14
Displaying a Matrix
To display the contents of a matrix on the Home screen, copy the name
from the
MATRX NAMES
menu and press
Í
.
If all of a matrix answer does not fit in the display, as indicated by ellipsis
marks in the left or right column or
#
or
$
in the right column, use
~
,
|
,
†
,
and
}
to display the rest of the matrix.
Copying One Matrix to Another
To copy a matrix, store it to another matrix. (Access the names on the
MATRX NAMES
menu.)
Accessing a Matrix Element
You can store a value to (or recall a value from) a specific matrix element
on the Home screen or from a program. The element must be within the
currently defined matrix dimensions.
matrix(
row
,
column
)
10-10 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 10 of 14
Matrix Math Functions
You can use many of the math functions on the keyboard, MATH MATH menu,
and the MATH NUM menu with matrices. However, the dimensions must be
appropriate.
+ (Add), – (Subtract)
To add (
Ã
) or subtract (
¹
) matrices, the dimensions must be the same.
The answer is a matrix in which the elements are the sum or difference of
the individual elements.
matrixA
+
matrixB
matrixA
–
matrixB
…
(
Multiply)
To multiply (
¯
) two matrices together, the column dimension of
matrixA
must match the row dimension of
matrixB
.
matrixA
…
matrixB
Multiplying a
matrix
by a
value
or a
value
by a
matrix
returns a matrix in
which each element of
matrix
is multiplied by
value
.
matrix
…
value
value
…
matrix
M
(Negate)
Negating a matrix (
Ì
) returns a matrix in which the sign of every element
is changed (reversed).
M
matrix
abs
abs
(absolute value,
y
ã
ABS
ä
) returns a matrix containing the absolute
value of each element of
matrix
.
abs
matrix
Matrices 10-11
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 11 of 14
round(
round(
(
MATH NUM
menu) returns a matrix. It rounds every element in
matrix
to
#decimals
. If
#decimals
is omitted, the elements are rounded to
10 digits.
round(
matrix
,
#decimals
)
round(
matrix
)
-1
(Inverse)
Use the
-1
function (
—
) to invert a matrix (
^
M
1
is not valid).
matrix
must
be square. The determinant cannot equal zero.
matrix
-1
Powers
To raise a matrix to a power,
matrix
must be square. You may use
2
,
3
, or
^
n
(
n
between
0
and
255
).
matrix
2
matrix
3
matrix
^
power
Relational Operations
To compare two matrices using the relational operations
=
and
ƒ
, they must
have the same dimensions.
=
and
ƒ
compare
matrixA
and
matrixB
on an
element-by-element basis. The other relational operations are not valid with
matrices.
matrixA
=
matrixB
returns
1
if every comparison is true; it returns
0
if any
comparison is false.
matrixA
ƒ
matrixB
returns
1
if at least one comparison is false.
iPart, fPart, int
iPart
,
fPart
, and
int
(
MATH NUM
menu) return a matrix containing the
integer part, fractional part, or greatest integer of each element of
matrix
.
iPart
matrix
fPart
matrix
int
matrix
10-12 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 12 of 14
MATRX MATH Operations
Pressing
~
accesses the matrix math operations on the MATRX MATH
menu.
MATRX MATH Menu
NAMES MATH EDIT
1: det
Calculates the determinant.
2:
T
Transposes the matrix.
3: dim
Returns the matrix dimension.
4: Fill(
Fills all elements with a constant.
5: identity
Returns the identity matrix.
6: randM(
Returns a random matrix.
7: augment(
Augments two matrices.
8: rowSwap(
Swaps two rows of a matrix.
9: row+(
Adds two rows, stores in second row.
0:
…
row(
Multiplies row by a number.
A:
…
row+(
Multiplies row, adds to second row.
det
det
(determinant) returns the determinant (a real number) of a square
matrix
.
det
matrix
T
(Transpose)
T
(transpose) returns a matrix in which each element(
row
,
column
) is
swapped with the corresponding element(
column
,
row
) of
matrix
.
matrix
T
Accessing Matrix Dimensions with dim
dim
(dimension) returns a list containing the dimensions (
{
rows columns
}
)
of
matrix
.
dim
matrix
Note:
dim
matrix
!
L
n
:L
n
(1)
returns the number of rows.
dim
matrix
!
L
n
:L
n
(2)
returns the number of columns.
Matrices 10-13
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 13 of 14
Creating a Matrix with dim
dim
(
MATRIX MATH
item
3
) is used with
¿
to create new
matrixname
of dimensions
rows
×
columns
with all elements equal to zero.
{
rows
,
columns
}
!
dim
matrixname
Redimensioning a Matrix with dim
dim
is used with
¿
to redimension existing
matrixname
to dimensions
rows
×
columns
. The elements in the old
matrixname
that are within the
new dimensions are not changed. Any additional elements that are created
are zeros.
{
rows
,
columns
}
!
dim
matrixname
Fill(
Fill(
(
MATRIX MATH
item
4
) stores
value
to every element in
matrixname
.
Fill(
value
,
matrixname
)
identity
identity
(
MATRIX MATH
item
5
) returns the identity matrix of
dimension
rows ×
dimension
columns.
identity
dimension
randM(
randM(
(create random matrix,
MATRIX MATH
item
6
) returns a
rows
×
columns
matrix of random one-digit integers (
L
9 to 9). The values
are controlled by the
rand
function.
randM(
rows
,
columns
)
10-14 Matrices
8210MTRX.DOC TI-82, Chapter 10, English Bob Fedorisko Revised: 02/09/01 9:18 AM Printed:
02/09/01 12:38 PM Page 14 of 14
augment(
augment(
(
MATRIX MATH
item
7
) concatenates
matrixA
and
matrixB
. The
number of rows in
matrixA
must equal the number of rows in
matrixB
.
augment(
matrixA
,
matrixB
)
Row Operations
The row operations, which can be used in an expression, do not change
matrix
in memory. All row numbers and values can be entered as
expressions.
rowSwap(
rowSwap(
(
MATRIX MATH
item
8
) returns a matrix. It swaps
rowA
and
rowB
of
matrix
.
rowSwap(
matrix
,
rowA
,
rowB
)
row+(
row+(
(row addition,
MATRIX MATH
item
9
) returns a matrix. It adds
rowA
and
rowB
of
matrix
and stores the answer in
rowB
.
row+(
matrix
,
rowA
,
rowB
)
…
row(
…
row(
(row multiplication,
MATRIX MATH
item
0
) returns a matrix. It
multiplies
row
of
matrix
by
value
and stores the answer in
row
.
…
row(
value
,
matrix
,
row
)
…
row+(
…
row+(
(multiply and add row,
MATRIX MATH
item
A
) returns a matrix. It
multiplies
rowA
of
matrix
by
value
, adds it to
rowB
, and stores the answer
in
rowB
.
…
row+(
value
,
matrix
,
rowA
,
rowB
)
Lists 11-1
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 1 of 10
Chapter 11: Lists
This chapter describes the list features of the TI
.
82. The TI
.
82 can store up to six
lists. A list, depending on available memory, may have up to 99 elements.
Chapter Contents
Getting Started: Generating a Sequence
............
11-2
About Lists
.................................
11-3
LIST OPS
Operations
..........................
11-6
LIST MATH
Operations
.........................
11-9
11-2 Lists
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 2 of 10
Getting Started: Generating a Sequence
Getting Started is a fast-paced introduction. Read the chapter for details.
Calculate the first eight terms of the sequence 1
à
N
2
and display in fractional
form.
1. Begin on a blank line on the Home screen.
Press
y
ã
LIST
ä
to display the
LIST OPS
menu.
2. Press
5
to select
seq(
. The function name is
copied to the cursor location on the Home
screen.
3. Press
1
¥
ƒ
A
¡
¢
ƒ
A
¢
1
¢
8
¢
1
¤
¿
y
ã
L
1
ä
. Press
Í
to
generate the list and store it in
L
1
. The list is
displayed on the Home screen.
4. Use
~
to scroll the list to see all of the
elements.
5. Press
1
(to select
4
Frac
). On the Home
screen,
Ans
is typed automatically, followed
by
4
Frac
.
6. Press
Í
to show the sequence in
fractional form. Use
~
to scroll the list to
see all of the elements.
Lists 11-3
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 3 of 10
About Lists
The TI
.
82 has six list variables in memory: L
1
, L
2
, L
3
, L
4
, L
5
, and L
6
. On the Home
screen or in a program, you can use, enter, store, and display lists. The list
names are on the keyboard.
Using a List in an Expression
To use a list in an expression, you may:
¦
Use the name of the list (
L
1
,
L
2
,
L
3
,
L
4
,
L
5
, or
L
6
).
¦
Enter the list directly (see below).
¦
Press
y
ã
RCL
ä
, enter the name of the list, and then press
Í
to
recall the contents of the list into the expression at the cursor location.
Entering a List in an Expression
1. Press
y
ã
{
ä
to indicate the beginning of the list.
2. Enter a value (which can be an expression) for each element in the list,
separated by commas.
3. Press
y
ã
}
ä
to indicate the end of the list.
The expression is evaluated when the entry is executed. Commas are
required on entry to separate elements, but are not displayed on output.
The closing
}
is not necessary at the end of an expression or preceding
!
.
Saving a List in Memory
You can save a list in memory in two ways:
¦
Enter the list in the
STAT
list editor (Chapter 12).
¦
Enter the list on a blank line on the Home screen or in a program (see
above), press
¿
, and then enter the name of the list (
L
1
,
L
2
,
L
3
,
L
4
,
L
5
, or
L
6
).
11-4 Lists
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 4 of 10
Displaying a List
To display the contents of a list on the Home screen, enter the name of the
list and press
Í
.
If all of a list answer does not fit in the display on the Home screen, as
indicated by ellipsis marks in the left or right column, use
~
and
|
to
display the rest of the list.
Copying One List to Another
To copy a list, store it to another list.
Accessing a List Element
You can store a value to (or recall a value from) a specific list element.
Enter the name of the list, followed by the number of the element in
parentheses. You can store to any element within the currently defined list
dimensions or one beyond.
listname
(
element
)
Lists in Graphing
In graphing, lists are used to graph a family of curves (Chapter 3).
Lists 11-5
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 5 of 10
Notes about Using Math Functions with Lists
A list can be used to input several values for certain functions. (Other
chapters and Appendix A state if a list is valid.) The function is evaluated
for each element in the list, and a list is returned.
¦
If a list is used with a function, the function must be valid for every
element in the list, except in graphing. (In graphing, an invalid element
in a list, such as
M
1
in
‡
{1,0,
M
1}
, is simply ignored.)
)
This returns an error.
)
This graphs
X
…‡
1
and
X
…‡
0
, but
skips
X
…‡M
1
.
¦
If two lists are used with a two-argument function, the length of the lists
must be the same. The answer is a list in which each element is
calculated by evaluating the function using the corresponding elements
in the lists.
¦
If a list and a value are used with a two-argument function, the value is
used with each element in the list.
11-6 Lists
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 6 of 10
LIST OPS Operations
Pressing
y
9
accesses the list operations on the LIST OPS menu.
LIST OPS Menu
OPS MATH
1: SortA(
Sorts lists in ascending order.
2: SortD(
Sorts lists in descending order.
3: dim
Accesses the list dimension.
4: Fill(
Fills all elements with a constant.
5: seq(
Creates a sequence.
Note:
dim
and
Fill(
are the same as
dim
and
Fill(
on the
MATRX MATH
menu.
SortA(
and
SortD(
are the same as
SortA(
and
SortD(
on the
STAT EDIT
menu.
SortA(, SortD(
SortA(
(sort ascending) and
SortD(
(sort descending) have two uses.
¦
With one
listname
, they sort the elements of an existing list and update
the list in memory.
¦
With two to six
listnames
, they sort the first list and then sort the
remaining lists as dependent lists, element-by-element, and update the
lists in memory. All lists must be the same length.
SortA(
listname
)
SortA(
listnameI
,
listnameD
,
listnameD
,
. . .
)
Lists 11-7
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 7 of 10
Accessing List Dimensions with dim
dim
(dimension) returns the length (number of elements) of
list
.
dim
list
Creating a List with dim
dim
is used with
¿
to create new
listname
with dimension
length
. The
elements are zeros.
length
!
dim
listname
Redimensioning a List with dim
dim
is used with
¿
to redimension existing
listname
to dimension
length
.
¦
The elements in the old
listname
that are within the new dimension are
not changed.
¦
Any additional elements that are created are zeros.
length
!
dim
listname
11-8 Lists
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 8 of 10
Fill(
Fill(
(
LIST OPS
item
4
) stores
value
to each element in
listname
.
Fill(
value
,
listname
)
seq(
seq(
(sequence,
LIST OPS
item
5
) returns a list in which each element is
the value of
expression
, evaluated at
increment
s for
variable
from
begin
to
end
.
seq(
expression
,
variable
,
begin
,
end
,
increment
)
variable
need not be defined in memory.
increment
can be negative.
seq(
is
not valid in the
expression
.
U
n
or
V
n
is not valid in
expression
. To generate a sequence from
U
n
or
V
n
,
use
U
n
(
nstart
,
nstop
,
nstep
)
.
Lists 11-9
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 9 of 10
LIST MATH Operations
Pressing
y
9
~
accesses the list math operations on the LIST MATH menu.
LIST MATH Menu
OPS MATH
1: min(
Returns minimum element of a list.
2: max(
Returns maximum element of a list.
3: mean(
Returns mean of a list.
4: median(
Returns median of a list.
5: sum
Returns sum of all elements in list.
6: prod
Returns product of all elements in list.
Note:
min(
and
max(
are the same as
min(
and
max(
on the
MATH NUM
menu.
min(, max(
min(
(minimum) and
max(
(maximum) return the smallest or largest
element of
list
. If two lists are compared, it returns a list of the larger of
each pair of elements in
listA
and
listB
.
min(
list
)
or
max(
list
)
min(
listA
,
listB
)
or
max(
listA
,
listB
)
mean(, median(
mean(
returns the mean value of
list
.
median(
returns the median value of
list
.
mean(
list
)
or
median(
list
)
If a second list is given, it is interpreted as the
frequency
of the elements in
list
.
mean(
list
,
frequency
)
or
median(
list
,
frequency
)
11-10 Lists
8211LIST.DOC TI-82, Chapter 11, English Bob Fedorisko Revised: 02/09/01 12:25 PM Printed: 02/09/01
12:38 PM Page 10 of 10
sum
sum
(summation,
LIST MATH
item
5
) returns the sum of the elements in
list
.
sum
list
prod
prod
(
LIST MATH
item
6
) turns product of the elements of
list
.
prod
list
Sums and Products of Numeric Sequences
You can combine
sum
or
prod
with
seq(
to obtain:
upper upper
G
expression
(
x
)
∏
expression
(
x
)
x=lower x=lower
To evaluate
G
2
(N–1)
from N=1 to 4:
Statistics 12-1
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 1 of 22
Chapter 12: Statistics
This chapter describes the tools for analyzing statistical data on the TI
.
82. These
include entering lists of data, calculating statistical results, fitting data to a
model, and plotting data.
Chapter Contents
Getting Started: Building Height and City Size
........
12
-
2
Setting Up a Statistical Analysis
..................
12
-
9
Viewing List Elements
.........................
12
-
10
Editing List Elements
.........................
12
-
11
STAT EDIT
Menu
.............................
12
-
12
Statistical Analysis
...........................
12
-
13
Statistical Variables
...........................
12
-
14
Types of Statistical Analysis
.....................
12
-
15
Statistical Analysis in a Program
.................
12
-
17
Statistical Plotting
............................
12
-
18
Statistical Plotting in a Program
..................
12
-
22
12-2 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 2 of 22
Getting Started: Building Height and City Size
Getting Started is a fast-paced introduction. Read the chapter for details.
Determine a linear equation to fit the data below. Enter and plot the data and
determine the best line, then predict how many buildings of more than 12 stories
you would expect to find in a city of 300,000 people. Begin by entering the data in
the STAT list editor and sorting it.
Population Buildings>12 stories
150,000 4
500,000 31
800,000 42
250,000 9
500,000 20
750,000 55
950,000 73
1. To clear any existing lists, press
…
4
(to copy
ClrList
to the Home screen) and then press
y
ã
L
1
ä
¢
y
ã
L
2
ä
¢
y
ã
L
3
ä
¢
y
ã
L
4
ä
¢
y
ã
L
5
ä
¢
y
ã
L
6
ä
Í
.
2. Press
…
to display the
STAT EDIT
menu.
3. Press
1
(to select
Edit...
). The
STAT
list editor is
displayed.
Press
150000
. As you type, the value is displayed
on the bottom line.
4. Press
Í
. The value is shown in the first
element of
L
1
and the cursor moves to the
second element in the same list.
Press
500000
Í
800000
Í
250000
Í
500000
Í
750000
Í
950000
Í
to
enter the remaining elements of
L
1
.
Statistics 12-3
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 3 of 22
5. Press
~
to move to the first element of list
L
2
.
6. Press
4
Í
31
Í
42
Í
9
Í
20
Í
55
Í
73
Í
to enter the elements
of
L
2
.
7. You can sort the data by size of city. Press
…
2
(to select
SortA(
, which is copied to the Home
screen)
y
ã
L
1
ä
(to select the independent list)
¢
y
ã
L
2
ä
(to select the dependent list)
¤
Í
.
8. The lists have been updated in memory. Press
…
1
to use the
STAT
list editor to display the
lists.
12-4 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 4 of 22
After entering and sorting the data, set up the statistical calculations, then
perform the calculations, storing the equations in the Y= list.
9. Press
…
~
to display the
STAT CALC
menu.
10. Press
3
(to select
SetUp...
).
The
SET UP CALCS
screen appears.
Xlist
for
2-Var
should be
L
1
;
Ylist
should be
L
2
; and
Freq
should be
1
.
11. Press
…
~
4
(to select
Med
.
Med
). The
instruction is copied to the Home screen. Press
Í
to calculate a line fitting the data using
the
SET UP CALCS
settings. The model
coefficients are displayed on the Home screen.
12. In
Func
MODE
, press
o
to display the
Y=
editor. Clear
Y
1
and
Y
2
if necessary.
Press
to display the
VARS
screen.
Statistics 12-5
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 5 of 22
13. Press
5
(to select
Statistics...
) and
~
~
to
display the
VARS EQ
menu.
14. Press
7
(to select
RegEQ
). The regression
equation for the current model equation (which
was calculated using
Med
.
Med
) is copied to
Y
1
.
15. Press
…
~
5
(to select
LinReg(ax+b)
). The
instruction is copied to the Home screen. Press
Í
to calculate the least-squares linear
regression.
16. Press
o
(to display the
Y=
editor)
Í
(to
move to
Y
2
)
(to display the
VARS
menu)
5
(to select
Statistics...
)
~
~
(to display the
VARS EQ
menu)
7
(to select
RegEQ
). The
current model equation (calculated using
LinReg(ax+b)
) is copied to
Y
2
.
12-6 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 6 of 22
To plot statistical data, you must enter the data in lists and then define the plot. If
you have done calculations to fit the data to one or more models and stored the
resulting equations in the Y= list, the data and the equations can be shown and
traced simultaneously.
17. Press
y
ã
STAT PLOT
ä
to display the
STAT PLOTS
screen.
18. Press
1
(to display the
Plot1
screen). Press
Í
to turn
Plot1
On
. Leave
Type
as a scatter
plot,
Xlist
as
L
1
, and
Ylist
as
L
2
and
Mark
as a ›.
19. Press
q
9
(to select
ZoomStat
).
ZoomStat
examines the data for all currently selected
Stat Plots
and adjusts the viewing
WINDOW
to
include all points, which are shown on the
current graph. (This also plots the regression
equations in
Y
1
and
Y
2
.)
20. Press
r
. Press
~
to trace the points in
Plot1
, as indicated by
P
1
in the upper right
corner of the display.
Press
†
to move to
Y
1
. Press
†
again to move
to
Y
2
.
Statistics 12-7
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 7 of 22
You can enter expressions to define lists in the STAT list editor. For example, you
can define predicted values and residuals.
21. To tell which line better fits the data, look at the
residuals for both models. Press
…
1
to
display the
STAT
list editor. Press
~
~
}
to
move the cursor onto the name
L
3
.
Press
y
ã
Y-VARS
ä
1
(to select
Function...
)
1
(to
select
Y
1
)
£
y
ã
L
1
ä
¤
. This defines
L
3
as the
values predicted by the
Med
.
Med
line.
22. Press
Í
to store the values in
L
3
.
23. To store the residuals for
Med
.
Med
in
L
4
, press
~
}
(to move the cursor onto the name
L
4
)
y
ã
L
2
ä
(the observed)
¹
y
ã
L
3
ä
(the predicted)
Í
.
24. Press
~
}
to move onto
L
5
. Press
y
ã
Y-VARS
ä
1
(to select
Function...
)
2
(to select
Y
2
)
£
y
ã
L
1
ä
¤
Í
. This defines
L
5
as the values
predicted by the
LinReg(ax+b)
line.
25. Press
~
}
(to move the cursor onto the name
L
6
)
y
ã
L
2
ä
(the observed)
¹
y
ã
L
5
ä
(the
predicted)
Í
to evaluate and store the
residuals for
LinReg(ax+b)
in
L
6
.
12-8 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 8 of 22
You can use the TI
.
82 to compare different models on the same data set.
26. Press
y
ã
STAT PLOT
ä
. Press
1
to select
Plot1
.
Press
~
Í
to turn the plot off.
Press
y
ã
STAT PLOT
ä
. Press
2
to select
Plot2
.
Press
Í
to turn the plot on. Press
†
†
Í
to define
Xlist
as
L
1
. Press
†
~
~
~
Í
to define
Ylist
as
L
4
. Leave
Mark
as
›
.
27. Press
y
ã
STAT PLOT
ä
. Press
3
to select
Plot3
.
Press
Í
to turn the plot on. Press
†
†
Í
to define
Xlist
as
L
1
. Press
†
~
~
~
~
~
Í
to define
Ylist
as
L
6
. Press
†
~
Í
to
define
Mark
as
+
.
Press
y
ã
STAT PLOT
ä
to view the settings.
28. Press
o
|
Í
†
Í
to turn off
Y
1
and
Y
2
.
Press
q
9
to plot the residuals.
›
marks the
residuals from
Med
.
Med
and
+
marks the
residuals from
LinReg
.
29. Press
y
ã
QUIT
ä
to return to the Home screen.
Press
~
1
(to select
round(
)
y
ã
Y-VARS
ä
1
(to select
Function...
)
1
(to select
Y
1
)
£
300000
¤
¢
0
¤
Í
. The value of
Y
1
(
Med
.
Med
model) for
X
=300,000, rounded to 0
decimal places (whole buildings), is shown.
Press
y
ã
ENTRY
ä
}
~
y
ã
Y-VARS
ä
1
2
Í
.
The value of
Y
2
(
LinReg(ax+b)
model) for
X
=300,000 is shown.
Statistics 12-9
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 9 of 22
Setting Up a Statistical Analysis
The data for statistical analyses is stored in lists. The TI
.
82 has six list variables
in memory that you can use in stat calculations. Several types of statistical
analyses are available.
Steps
1. Enter the stat data in list(s) (pages 12
.
9 through 12
.
12).
2. Set up statistical calculations (page 12
.
13).
3. Calculate the statistical variables or fit the data to a model (page 12
.
14
through 12
.
17).
4. Plot the data (page 12
.
18 through 12
.
21).
Displaying the STAT List Editor
To display the
STAT
list editor, press
…
and then press
1
or
Í
to
select
Edit...
from the
STAT EDIT
menu.
The top line displays the names of the lists (even if the list is empty). The
center portion of the
STAT
list editor displays up to seven elements of three
lists, showing the values of the elements in abbreviated form if necessary.
The full value of the current element (indicated by the rectangular cursor)
is shown on the bottom line.
Leaving the STAT List Editor
To leave the
STAT
list editor:
¦
Select another screen by pressing the appropriate key.
¦
Press
y
ã
QUIT
ä
to return to the Home screen.
Deleting a List
You can delete the contents of a list in several ways:
¦
Use the
ClrList
instruction (page 12
.
12).
¦
Through the
MEM
menu (Chapter 16).
¦
In the
STAT
editor, press
}
to move onto the list name, and press
‘
Í
.
¦
In the
STAT
editor, delete each element.
¦
On a command line, enter
0
!
dim
listname
.
12-10 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 10 of 22
Viewing List Elements
The STAT list editor has two “contexts,” viewing and editing. The current context
determines the result of a keystroke.
Viewing Context Keys
In viewing context, you can move quickly from one list element to the next.
The full value of the current element is displayed on the bottom line.
|
or
~
Moves the rectangular cursor within the current row.
†
or
}
Moves the rectangular cursor within the current
column. On row 1,
}
moves the cursor to the list name
and shows the entire list in display input format, but the
list cannot be scrolled).
Í
Switches to editing context; activates the edit cursor on
the bottom line.
‘
Switches to editing context; clears the value on the
bottom line.
A
ny entry
character
Switches to editing context; clears the value on the
bottom line; copies the character to the bottom line.
y
[
INS
] Inserts a list element (value is zero).
{
Deletes the current list element (closes up list).
Statistics 12-11
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 11 of 22
Editing List Elements
In the editing context, an edit cursor is active on the bottom line, and you can
change the value of the current list element. You can also move onto the list
name and edit the entire list at once.
Editing Context Keys
|
or
~
Moves the edit cursor within the value.
‘
Clears the value on the bottom line.
A
ny entry
character
Copies the character to the location of the edit cursor
on the bottom line. If it is the first character typed, the
v
alue on the bottom line is cleared.
y
[
INS
] Activates insert cursor.
{
Deletes character.
Í
Stores the value on the bottom line to the list element;
switches to viewing context. Rectangular cursor moves
to the next element.
†
or
}
Stores the value on the bottom line to the list element;
switches to viewing context and moves the rectangular
cursor within the column.
Editing a List Element
1. Move the rectangular cursor to the element you want to change.
2. Switch to editing context.
¦
Press
Í
to change the value by inserting, deleting, or typing over
digits.
¦
Press
‘
to clear the entire value so you can enter a new value.
Note: You can press
‘
, followed by
Í
to restore the value
at the rectangular cursor if you make a mistake.
¦
Press an entry key, such as a number or letter, to begin an entry. This
automatically clears the value.
3. Enter the value. You may enter an expression (which is evaluated when
you leave editing context).
4. Press
Í
,
}
, or
†
to move to another element.
12-12 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 12 of 22
STAT EDIT Menu
Pressing
…
accesses the STAT list editor and several instructions for use with
lists.
STAT EDIT Menu
EDIT CALC
1: Edit
…
Displays list editor (page 12
.
9).
2: SortA(
Sorts list in descending order.
3: SortD(
Sorts list in ascending order.
4: ClrList
Deletes all elements of list.
Note:
SortA(
and
SortD(
are the same as
SortA(
and
SortD(
on the
LIST OPS
menu.
SortA(, SortD(
SortA(
(sort ascending) and
SortD(
(sort descending) have two uses.
¦
With one
listname
, they sort the elements of an existing list and update
the list in memory.
¦
With two to six
listnames
, they sort the first list and then sort the
remaining lists as dependent lists, element by element, and update the
lists in memory. All lists must be the same length.
SortA(
listname
)
SortA(
listnameI
,
listnameD
,
listnameD
,
. . .
)
ClrList
ClrList
clears (deletes) the elements of one or more
listnames
.
ClrList
listnameA
,
listnameB
,
. . .
Statistics 12-13
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 13 of 22
Statistical Analysis
Pressing
…
~
accesses the STAT CALC menu, where you set up and perform
statistical calculations. The TI
.
82 can analyze one-variable or two-variable
statistics. Both can have associated frequencies.
STAT CALC Menu
EDIT CALC
1: 1-Var Stats
Calculates 1-variable statistics.
2: 2-Var Stats
Calculates 2-variable statistics.
3: SetUp
…
Defines lists to use in calculations.
4: Med-Med
Calculates median-median line.
5: LinReg(ax+b)
Fits data to linear model.
6: QuadReg
Fits data to quadratic model.
7: CubicReg
Fits data to cubic model.
8: QuartReg
Fits data to quartic model.
9: LinReg(a+bx)
Fits data to linear model.
0: LnReg
Fits data to logarithmic model.
A: ExpReg
Fits data to exponential model.
B: PwrReg
Fits data to power model.
SET UP CALCS Screen
When you select
SetUp...
, the
SET UP CALCS
screen appears, where you
can define a statistical analysis.
¦
1-Var Stats
(one-variable statistics) analyzes data with one measured
variable.
¦
2-Var Stats
(two-variable statistics) analyzes paired data between
which there is a relationship.
Xlist
is the independent variable.
Ylist
is
the dependent variable.
¦
Freq
(frequency of occurrence) is a list of integers between 0 and 99
(inclusive).
Freq
is optional; the default is
1
. It is valid for one-variable
or two-variable statistics.
Note: You can override
SET UP CALCS
settings by specifying the name(s)
of the list(s) after the statistical calculation instruction (Appendix A).
Changing Settings
To change a setting on the
SET UP CALCS
screen, use
†
,
}
,
~
, and
|
to
position the cursor and then press
Í
.
12-14 Statistics
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 14 of 22
Statistical Variables
The statistical variables are calculated as indicated below. Some are displayed
when 1-Var Stats or 2-Var Stats are calculated. You can access these variables
for use in expressions through the
Statistics... menus. If a list is edited or
the type of analysis is changed, all statistical variables are cleared.
Variables
1-Var
Stats
2-Var
Stats
Other
VARS
Menu
mean of
x
values
vv
X/Y
sum of
x
values
G
x
G
x
G
sum of
x
2
values
G
x
2
G
x
2
G
sample standard deviation of
xSxSx
X/Y
population standard deviation of
x
s
x
s
x
X/Y
number of data points
nn
X/Y
mean of
y
values
w
X/Y
sum of
y
values
G
y
G
sum of
y
2
values
G
y
2
G
sample standard deviation of
ySy
X/Y
population standard deviation of
y
s
y
X/Y
sum of
x
…
y
G
xy
G
minimum of
x
values
minX minX
X/Y
maximum of
x
values
maxX maxX
X/Y
minimum of
y
values
minY
X/Y
maximum of
y
values
maxY
X/Y
1st quartile
Q
1
BOX
median
Med
BOX
3rd quartile
Q
3
BOX
regression/fit coefficients
a
,
b
EQ
polynomial coefficients
a
,
b
,
c
,
d
,
e
EQ
correlation coefficient
r
EQ
regression equation
RegEQ
EQ
summary points (
Med
.
Med
only)
x
1
,
y
1
,
x
2
,
y
2
,
x
3
,
y
3
PTS
Q
1
and Q
3
The quartile
Q
1
is the median of the ordinals to the left of
Med
. The quartile
Q
3
is the median of the ordinals to the right of
Med
.
Statistics 12-15
8212STAT.DOC TI-82, Chapter, English Bob Fedorisko Revised: 02/09/01 9:23 AM Printed: 02/09/01
12:42 PM Page 15 of 22
Types of Statistical Analysis
The SET UP CALCS settings are used for statistical analyses. You can override
SET UP CALCS settings by specifying the name(s) of the list(s) and frequency
after the statistical calculation instruction (Appendix A).
1-Var Stats
1-Var Stats
(one-variable statistics,
STAT CALC
item
1
) calculates
statistical variables as indicated on the previous page.
2-Var Stats
2-Var Stats
(two-variable statistics,
STAT CALC
item
2
) calculates
statistical variables as indicated on the previous page.
Med
.
Med
Med
.
Med
(median-median,
STAT CALC
item
4
) fits the data to the model
y=ax+b
using the median-median line (resistant line) technique, calculating
the summary points
x
1
,
y
1
,
x
2
,
y
2
,
x
3
, and
y
3
. It displays
a
(slope) and
b
(
y
-intercept).
LinReg (ax+b)
LinReg (ax+b)
(linear regression,
STAT CALC
item
5
) fits the data to the
model
y=ax+b
using a least-squares fit and
x
and
y
. It displays
a
(slope),
b
(
y
-intercept), and
r
(correlation coefficient).
QuadReg
QuadReg
(quadratic regression,
STAT CALC
item
6
) fits the data to the
second-order polynomial
y=ax
2
+bx+c
. It displays
a
,
b
, and
c
. For three
points the equation is a polynomial fit; for four or more, it is a polynomial
regression. At least three points are required.
CubicReg
CubicReg
(cubic regression,
STAT CALC
item
7
) fits the data to the third-
order polynomial
y=ax
3
+bx
2
+cx+d
. It displays
a
,
b
,
c
, and
d
. For four points
the equation is a polynomial fit; for five or more, it is a polynomial
regression. At least four points are required.
QuartReg
QuartReg
(quartic regression,
STAT CALC
item
8
) fits the data to the
fourth-order polynomial
y=ax
4
+bx
3
+cx
2
+dx+e
. It displays
a
,
b
,
c
,
d
, and
e
.
For five points the equation is a polynomial fit; for six or more, it is a
polynomial regression. At least five points are required.
12-16 Statistics
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LinReg (a+bx)
LinReg (a+bx)
(linear regression,
STAT CALC
item
9
) fits the data to the
model equation
y=a+bx
using a least-squares fit and
x
and
y
. It displays
a
(
y
-intercept),
b
(slope), and
r
(correlation coefficient).
LnReg
LnReg
(logarithmic regression,
STAT CALC
item
0
) fits the data to the
model equation
y=a+b ln(x)
using a least-squares fit and transformed values
ln(x)
and
y
. It displays
a
,
b
, and
r
(correlation coefficient).
ExpReg
ExpReg
(exponential regression,
STAT CALC
item
A
) fits the data to the
model equation
y=ab
x
using a least-squares fit and transformed values
x
and
ln(y)
. It displays
a
(
y
-intercept),
b
, and
r
(correlation coefficient).
PwrReg
PwrReg
(power regression,
STAT CALC
item
B
) fits the data to the model
equation
y=ax
b
using a least-squares fit and transformed values
ln(x)
and
ln(y)
. It displays
a
,
b
, and
r
(correlation coefficient).
Statistics 12-17
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Statistical Analysis in a Program
You can enter statistical data, calculate statistical results, and fit data to models
from a program.
Entering Stat Data
Enter statistical data into lists directly (Chapter 11).
Statistical Calculations
1. On a blank line in the program editor, select the type of calculation
from the
STAT CALC
menu.
2. You can enter the names of the lists to use in the calculation or use the
lists defined in
SET UP CALCS
. Note: You cannot access
SET UP CALCS
from the program editor.
12-18 Statistics
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Statistical Plotting
You can plot statistical data that you have entered in lists. The types of plots
available include scatter plots, x-y lines, box-and-whisker plots, and histograms.
You can define up to three plots at a time.
Steps
1. Enter the stat data in list(s) (page 12
.
9 through 12
.
12 and Chapter 11).
2. Set up statistical calculations (page 12
.
13) and calculate the statistical
variables or fit the data to a model (page 12
.
14 through 12
.
17), if
desired.
3. Select or deselect
Y=
equations as appropriate (Chapter 3).
4. Define the stat plot (page 12
.
21).
5. Turn plot(s) on, if necessary (page 12
.
21).
6. Define the viewing
WINDOW
(page 12
.
21 and Chapter 3).
7. Display and explore the graph (Chapter 3).
Scatter Plot
Scatter
plots the data points from
Xlist
and
Ylist
as coordinate pairs,
showing each point as a box (
›), cross (
+
), or dot (
¦
).
Xlist
and
Ylist
must be
the same length. They can be the same list.
Freq
does not apply.
xyLine
xyLine
is a
Scatter
plot in which the data points are plotted and connected
in the order in which they appear in
Xlist
and
Ylist
. You may want to sort the
lists with
SortA(
or
Sort(D
before plotting.
Statistics 12-19
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Boxplot
Boxplot
plots one-variable data. The whiskers on the plot extend from the
minimum data point in the set (
minX
) to the first quartile (
Q
1
) and from the
third quartile (
Q
3
) to the maximum point (
maxX
). The box is defined by
Q
1
,
the median (
Med
), and
Q
3
. (page 12
.
14)
Box plots ignore
Ymin
and
Ymax
, but are plotted with respect to
Xmin
and
Xmax
. When two box plots are plotted, the first plots in the middle and the
second plots in the bottom. When three box plots are plotted, the first plots
on the top and the third plots on the bottom.
Histogram
Histogram
plots one-variable data.
Xscl
determines the width of each bar,
beginning at
Xmin
.
ZoomStat
adjusts
Xmin
and
Xmax
to include all values,
but does not change
Xscl
.
(Xmax–Xmin)
à
Xscl
must be
47. A value
occurring on the edge of a bar is counted in the bar to the right.
12-20 Statistics
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12:42 PM Page 20 of 22
Defining the Plots
1. Press
y
ã
STAT PLOT
ä
. The
STAT PLOTS
screen shows the current plot
definitions.
2. Select the plot to define (
Plot1
,
Plot2
, or
Plot3
).
3. If you wish to plot the statistical data immediately, select
On
. You can
define a plot at any time and leave it
Off
. The definition will be available
in the future.
4. Select the type of plot. The options change appropriately:
¦
Scatter: Xlist Ylist Mark
¦
xyLine: Xlist Ylist Mark
¦
Boxplot: Xlist Freq
¦
Histogram: Xlist Freq
5. Depending on the type of plot, select the options:
¦
Xlist
(independent data)
¦
Ylist
(dependent data)
¦
Freq
(frequency,
1
is used if not specified)
¦
Mark
(›,
+
, or
¦
)
Statistics 12-21
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Turning Plots Off or On
PlotsOff
and
PlotsOn
allow you to turn stat plots on or off from the Home
screen or a program. Used without
plot#
, they turn all plots on or all plots
off. Used with
plot#
, they turn specific plots on or off.
PlotsOff
or
PlotsOn
PlotsOff
plot#
,
plot#
,
. . .
PlotsOn
plot#
For example,
PlotsOff:PlotsOn 3
turns all plots off and then turns
Plot3
on.
Defining the Viewing WINDOW
Stat plots are displayed on the current graph. You may define the viewing
WINDOW
by pressing
p
and then entering values for the
WINDOW
variables.
ZoomStat
redefines the viewing
WINDOW
so that all statistical data points
are displayed. For one-variable plots (
Histogram
and
Box plot
), only
Xmin
and
Xmax
are adjusted. If the top of the histogram is not shown, use
TRACE
to determine the value for
Ymax
.
Tracing a Stat Plot
When you
TRACE
a
Scatter
plot or
xyLine
, tracing begins at the first
element in the lists.
When you
TRACE
a
Box
plot, tracing begins at
Med
(the median). Press
|
to trace to
Q
1
and
minX
. Press
~
to trace to
Q
3
and
maxX
.
When you
TRACE
a
Histogram
, the cursor moves from the top center of
each column.
When you press
}
or
†
to move to another plot or
Y=
function, tracing
moves to the current or beginning point on that plot (not the nearest pixel).
12-22 Statistics
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Statistical Plotting in a Program
You may define a plot, select or deselect a plot, and display a plot from a program
Stat Plots
To display a stat plot, you may define the plot(s), then turn on the plot(s),
and then display the graph. (If you do not define the plot, the current
definitions are used).
For example:
Defining a Stat Plot
1. Begin on a blank line in the program editor. Press
y
ã
STAT PLOT
ä
to
display the
STAT PLOTS
menu.
2. Select the plot to define.
Plot1
,
Plot2
, or
Plot3
is copied to the cursor
location.
3. Press
y
ã
STAT PLOT
ä
~
to display the
STAT TYPES
menu. Select the
type of plot.
Scatter
,
xyLIne
,
Boxplot
, or
Histogram
is copied to the
cursor location.
4. Press
¢
then enter list names. See Appendix A for the appropriate
options.
5. Select the type of mark (for
Scatter
or
xyLine
).
Displaying a Stat Plot
To display a plot, use the
DispGraph
instruction or any of the
ZOOM
instructions.
Programming 13-1
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 1 of 18
Chapter 13: Programming
This chapter describes specific programming instructions and how to enter and
execute programs on the TI
.
82.
Chapter Contents
Getting Started: Family of Curves
.................
13-2
About TI
.
82 Programs
.........................
13-4
Creating and Executing Programs
................
13-5
Editing Programs
............................
13-6
PRGM CTL
(Control) Instructions
.................
13-7
PRGM I/O
(Input/Output) Instructions
..............
13-13
Calling Other Programs
........................
13-18
13-2 Programming
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Getting Started: Family of Curves
Getting Started is a fast-paced introduction. Read the chapter for details.
A program is a set of commands that can be executed sequentially, as if they had
been entered from the keyboard. Write a simple program to graph the family of
curves 2 sin X, 4 sin X, and 6 sin X.
1. Press
~
~
to display the
PRGM NEW
menu.
2. Press
Í
(to select
Create New...
). Type
S I N E S
as the name of the program (the
keyboard is in
ALPHA-LOCK
), and press
Í
.
You are now in the program editor. Note the
:
(colon) in the first column of the second line to
indicate that this is the beginning of a command
line.
3. Press
ƒ
ã
"
ä
(above
Ã
)
y
ã
{
ä
2
¢
4
¢
6
y
ã
}
ä
˜
„
ƒ
ã
"
ä
¿
y
ã
Y-VARS
ä
.
Press
Í
(to select
Function...
). Press
Í
(to select
Y
1
).
This instruction stores the function
{2,4,6}sin X
to
Y
1
.
4. Press
Í
to complete the instruction and
move to the next line. The
:
(colon) indicates the
beginning of the second command line.
5. Press
q
. The
ZOOM
menu appears, just as it
does elsewhere. Press
6
(to select
ZStandard
).
The instruction
ZStandard
is copied to the
cursor location. Press
Í
to complete the
instruction.
6. Press
r
. The instruction
Trace
is copied to
the cursor location. Press
Í
to complete the
instruction.
Programming 13-3
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 3 of 18
7. Press
y
ã
QUIT
ä
to return to the Home screen.
8. Press
to display the
PRGM
menu.
9. Select
SINES
. The instruction
prgmSINES
is
copied to the Home screen.
10. Press
Í
to execute the instruction. The
three curves are graphed immediately, then the
dotted “pause” indicator appears in the upper
right of the display to indicate that the program
will not resume execution until you press
Í
.
11. Use
|
,
}
,
~
, and
†
to trace the curves.
12. When you are done tracing, press
Í
. The
program continues. (In this case it ends.) The
graph remains on the screen for you to examine.
13. Press
o
to display the
Y=
editor. Notice that
Y
1
now contains the function you stored to it in the
program.
13-4 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
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About TI-82 Programs
Most features of the TI
.
82 are accessible from programs. Programs can access all
variables and named items. The number of programs that the TI
.
82 can store is
limited only by available memory.
Notes about Programs
On the TI
.
82, programs are identified by names, up to eight characters,
beginning with a letter.
A program consists of a series of program commands, which begin with a
:
(colon). A program command can be an expression or an instruction.
The TI
.
82 checks for errors when the program is executed, not as you enter
or edit the program.
Variables, lists, and matrices saved in memory are global. They can be
accessed from all programs. Storing a new value to a variable, list, or
matrix in a program changes the value in memory during program
execution.
As calculations are made in programs,
Ans
is updated, just as it would be if
the calculations were done on the Home screen. Programs do not update
Last Entry
as each command is executed.
"Breaking" a Program
É
stops program execution. When you press
É
to stop program
execution, the
ERR: BREAK
screen is displayed.
¦
To go to where the interrupt occurred, select
Goto
.
¦
To return to the Home screen, select
Quit
.
Memory Management and Erasing Programs
The size of programs you can store is limited only by available memory. To
access the memory management menu, press
y
ã
MEM
ä
from the Home
screen. Memory status is displayed on the
Check RAM...
screen. To increase
available memory, delete items, including other programs, from the
MEM DELETE FROM...
screen (Chapter 15).
Programming 13-5
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 5 of 18
Creating and Executing Programs
The program editor is accessed by pressing
and then choosing to create a
new program or edit an existing program.
Creating a New Program
1. Press
~
~
to display the
PRGM NEW
menu. Select
Create New
.
2. Enter the name you want for the program (the keyboard is in
ALPHA-LOCK
), followed by
Í
. The name may have one to eight
characters (
A
-
Z
,
0
-
9
,
q
) and must begin with a letter.
3. Enter the program instructions (page 13
.
6).
Editing a Program
1. Press
~
to display the
PRGM EDIT
menu.
2. Select the name of an existing program. The instructions in that
program are displayed.
3. Edit the program instructions (page 13
.
6).
Leaving the Program Editor
When you finish entering or editing a program, press
y
ã
QUIT
ä
to return to
the Home screen. You must be on the Home screen to execute a program.
Executing a Program
1. From a blank line on the Home screen, press
to display the
PRGM EXEC
menu.
2. Select the name of an existing program.
prgm
and the name of the
program are copied to the Home screen; for example,
prgmSINES
.
3. Press
Í
to begin execution of the program.
While the program is executing, the busy indicator is displayed.
13-6 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 6 of 18
Editing Programs
In general, anything that can be executed from the Home screen can be included
in a program, and vice versa. A program command always begins with a colon.
Entering Program Commands
A colon indicates the beginning of each program command. To enter more
than one instruction on a line, separate them with a colon (Chapter 1), just
as on the Home screen. Press
Í
to indicate the end of a command line.
An instruction may be longer than one line on the screen; if so, it will wrap
to the next screen line.
y
|
and
y
~
move the cursor to the beginning and end of a command
line.
In the program editor, if you press a key that accesses a menu, the menu
screen temporarily replaces the program edit screen. When you make a
selection or press
‘
, you are returned to the program editor.
Changing
Move the cursor to the command.
¦
Position the cursor and then make the changes.
¦
Press
‘
to clear (blank) all program commands on the command
line (the leading colon is not deleted), and then enter a new program
command.
Inserting
To insert a new command line, position the cursor where you want the new
line, press
y
ã
INS
ä
to put the TI
.
82 in insert mode, and press
Í
.
Deleting
To delete a command line, press
‘
to clear the line and then press
{
to delete the colon.
Copying a Program
RCL
(Chapter 1) copies (inserts) all of the commands of one program into
another, which you then can edit.
¦
You can create templates for frequently used groups of instructions,
such as setting
WINDOW
variables.
¦
You can make copies of programs.
To recall a program, press
y
ã
RCL
ä
|
to display the
PRGM EXEC
menu, then select the name of the program and press
Í
.
Programming 13-7
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02/09/01 12:42 PM Page 7 of 18
PRGM CTL (Control) Instructions
The PRGM CTL (program control) instructions can be accessed only from within
the program editor (press
). They direct the flow within an executing
program. They make it easy to repeat or skip a group of commands during
program execution. When you select an item from the menu, the name is copied
to the cursor location.
PRGM CTL Menu
CTL I/O EXEC
1: If
Create conditional test.
2: Then
Used with
If
.
3: Else
Used with
If-Then
.
4: For(
Create incrementing loop.
5: While
Create conditional loop.
6: Repeat
Create conditional loop.
7: End
Signifies end of loop,
If-Then
, or
Else
.
8: Pause
Pause program execution.
9: Lbl
Define a label.
0: Goto
Go to a label.
A: IS>(
Increment and skip if greater than.
B: DS<(
Decrement and skip if less than.
C: Menu(
Define menu items and branches.
D: prgm
Execute a program as a subroutine.
E: Return
Return from a subroutine.
F: Stop
Stops execution.
Controlling Program Flow
Program control instructions tell the TI
.
82 which command to execute next
in a program.
If
,
While
, and
Repeat
check a
condition
that you define to
determine what command to execute next.
condition
frequently uses
relational or Boolean tests (Chapter 2) such as
If A<7:A+1
!
A
or
If N=1 and M=1:Goto Z
.
If
If
is used for testing and branching. If
condition
is false (zero), then the
command immediately following it is skipped. If
condition
is true
(nonzero), that command is executed.
If
instructions can be nested.
:If
condition
:
command if true
:
command
13-8 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
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If-Then
Then
following an
If
executes a group of commands if
condition
is true
(nonzero).
End
identifies the end of the group. (
PRGM CTL
item
2
)
:If
condition
:Then
:
command if true
:
command if true
:End
:
command
If-Then-Else
Else
following
If-Then
executes a group of commands if
condition
is false
(zero).
End
identifies the end of the group. (
PRGM CTL
item
3
)
:If
condition
:Then
:
command if true
:
command if true
:Else
:
command if false
:
command if false
:End
:
command
For(
For(
is used for looping and incrementing. It increments
variable
from
begin
to
end
, by
increment
.
increment
is optional (if not specified, 1 is
used) and can be negative (
end
<
begin
).
end
is a maximum or minimum
value not to be exceeded.
End
identifies the end of the loop.
For(
loops can
be nested. (
PRGM CTL
item
4
)
:For(
variable
,
begin
,
end
,
increment
)
:
command while end not exceeded
:
command while end not exceeded
:End
:
command
For example,
For(A,0,10,2):Disp A
2
:End
, displays
0
,
4
,
16
,
36
,
64
, and
100
.
Programming 13-9
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 9 of 18
While
While
performs a group of commands while
condition
is true.
condition
is
frequently a relational test (Chapter 2).
condition
is tested when
While
is
encountered. If
condition
is true (nonzero), the program executes a group
of commands.
End
signifies the end of the group. If
condition
is false
(zero), the program executes the commands following
End
.
While
instructions can be nested. (
PRGM CTL
item
5
)
:While
condition
:
command while condition is true
:
command while condition is true
:End
:
command
Repeat
Repeat
repeats a group of commands until
condition
is true (nonzero). It is
similar to
While
, but
condition
is tested when
End
is encountered; thus the
group of commands will always be executed at least once.
Repeat
instructions can be nested. (
PRGM CTL
item
6
)
:Repeat
condition
:
command until condition is true
:
command until condition is true
:End
:
command
End
End
identifies the end of a group of commands. Each
For
,
While
,
Repeat
, or
Else
loop must have an
End
at the “bottom,” as must a
Then
loop without
an associated
Else
. (
PRGM CTL
item
7
)
13-10 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
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Pause
Pause
suspends execution of the program so you can see answers or
graphs. During the pause, the dotted pause indicator displays. Press
Í
to resume execution. (
PRGM CTL
item
8
)
¦
Pause
with no
value
temporarily pauses the program. If the instruction
DispGraph
or
Disp
has been executed, then the appropriate screen is
displayed.
¦
Pause
value
displays
value
, which can be scrolled, on the current Home
screen.
Lbl, Goto
Lbl
(label) and
Goto
(go to) are used together for branching.
Lbl
specifies the
label
of a command.
label
is one character (A
-
Z, 0
-
9, or
q
).
(
PRGM CTL
item
9
)
Lbl
label
Goto
causes the program to branch to
label
when the
Goto
is encountered.
(
PRGM CTL
item
0
)
Goto
label
IS>(
IS>(
(increment-and-skip) adds 1 to
variable
; if the answer is greater than
value
(which can be an expression), the next command is skipped.
variable
cannot be a system variable. (
PRGM CTL
item
A
)
:IS>(
variable
,
value
)
:
command if variable
value
:
command if variable
>
value
DS<(
DS<(
(decrement-and-skip) subtracts 1 from
variable
; if the answer is less
than
value
(which can be an expression), the next command is skipped.
variable
cannot be a system variable. (
PRGM CTL
item
B
)
:DS<(
variable
,
value
)
:
command if variable
‚
value
:
command if variable < value
Programming 13-11
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 11 of 18
Menu(
Menu(
sets up branching within a program. If
Menu(
is encountered during
execution, the menu screen is displayed with the specified menu items, the
dotted-bar pause indicator displays, and execution pauses until a menu
selection is made. (
PRGM CTL
item
C
)
The menu
title
is enclosed in
"
, followed by up to seven pairs of menu items
(
text
enclosed between
"
marks to display as the menu selection and the
label
to which to branch if that selection is made).
Menu("
title
","
text1
",
label1
,"
text2
",
label2
,
. . .
)
For example, during execution the instruction
Menu("TOSS DICE","FAIR DICE",A,"WEIGHTED DICE",B)
displays:
The program pauses until you select
1
or
2
. If you select
2
, for example, the
menu disappears and the program continues execution at
Lbl B
.
prgm
prgm
is used to enter instructions to execute other programs as
subroutines (page 13
.
18). When you select
prgm
, it is copied to the cursor
location. You may then type the letters of a program
name
. It is equivalent
to selecting existing programs from the
PRGM EXEC
menu, but allows you
to enter the name of a program that you have not yet created. (
PRGM CTL
item
D
)
prgm
name
Note: You cannot use this command with
RCL
(page 13
.
6).
13-12 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 12 of 18
Return
Return
quits the subroutine and returns to the calling program (page
13
.
18), even if encountered within nested loops. (Any loops are ended.)
There is an implied
Return
at the end of any program called as a
subroutine. Within the main program, it stops execution and returns to the
Home screen. (
PRGM CTL
item
E
)
Stop
Stop
stops execution of a program and returns you to the Home screen.
(
PRGM CTL
item
F
)
Programming 13-13
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 13 of 18
PRGM I/O (Input/Output) Instructions
The PRGM I/O (program input/output) instructions can be accessed only from
within the program editor (press
~
). They control input to and output from
a program during execution. They allow you to enter values and display answers
during program execution.
PRGM I/O Menu
CTL I/O EXEC
1: Input
Enter value or use free-moving cursor.
2: Prompt
Prompt for entry of variable values.
3: Disp
Display text, value, or Home screen.
4: DispGraph
Display the current graph.
5: DispTable
Display table.
6: Output(
Display text at a specified position.
7: getKey
Check the keyboard for a keystroke.
8: ClrHome
Clear the display.
9: ClrTable
Clear the current table.
0: PrintScreen
Print the current screen.
A: Get(
Gets variable from another device.
B: Send(
Sends variable to another device.
Input
¦
Input
without
variable
is used to display a graph on which you can use
the free-moving cursor.
¦
Input
with
variable
or
"
string
"
and
variable
is used to store a value to a
variable.
Displaying a Graph with Input
Input
without
variable
displays the current graph. You can move the free-
moving cursor, which updates
X
and
Y
(and
R
and
q
in
PolarGC FORMAT
).
The dotted-bar pause indicator is displayed. Press
Í
to resume
execution.
Storing a Variable Value with Input
Input
with
variable
prompts
?
during execution.
variable
may be a real
number, list, matrix or
Y=
function. Enter a value (which can be an
expression) and press
Í
. The value is evaluated and stored to
variable
,
and the program resumes execution. If
variable
is
Y
n
or other
Y=
functions,
enter
"
and then the expression, which will be stored to the
Y=
function as
entered.
Input
variable
You can display a
string
of up to 16 characters as a prompt. Enter a value
and press
Í
. The value is stored to
variable
, and the program resumes
execution.
Input "
string
",
variable
13-14 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 14 of 18
Disp
¦
Disp
(display) with no
value
displays the Home screen.
¦
Disp
with one or more
values
displays text and values.
Displaying the Home Screen
Disp
with no
value
displays the Home screen.
Disp
Displaying Values and Messages
Disp
with one or more
values
displays the value of each.
Disp
value
,
value
,
value
...
¦
If
value
is an expression, it is evaluated and then displayed on the right
of the following line according to the current
MODE
settings.
¦
If
value
is text (up to 16 characters) within
"
marks, it displays on the
left of the following line. Text cannot include
!
.
For example,
Disp "THE ANSWER IS",
pà
2
displays:
If
Pause
is encountered after
Disp
, the program halts temporarily so you
can examine the screen. Press
Í
to resume execution.
Note: If a matrix or list is too large to display in its entirety,
...
is displayed
in the rightmost column, but the matrix or list cannot be scrolled. (To
scroll, use the
Pause
instruction instead.)
Programming 13-15
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 15 of 18
Prompt
During execution
Prompt
displays each
variable
, one at a time, followed by
=?
. Enter a value and then press
Í
for each
variable
. The values are
stored, and the program resumes execution. (
PRGM I/O
item
2
)
Prompt
variableA
,
variableB
,
. . .
For example,
Prompt Xmin,Xmax,Ymin,Ymax
allows the user to enter
values for the viewing
WINDOW
.
If an expression is entered in response to
Prompt
, the expression is
evaluated and then stored.
Y
n
and other
Y=
functions are not valid with
Prompt
.
DispGraph
DispGraph
(display graph) displays the current graph. If
Pause
is
encountered after
DispGraph
, the program halts temporarily so you can
examine the screen. Press
Í
to resume execution. (
PRGM I/O
item
4
)
DispTable
DispTable
(display table) displays the current table. The program halts
temporarily so you can examine the screen. Press
Í
to resume
execution. (
PRGM I/O
item
5
)
Output(
Output(
displays
text
or a
value
on the current Home screen beginning at
line
(1–8) and
column
(1–16), typing over any existing characters. You may
wish to precede
Output(
with
ClrHome
(page 13
.
17). Expressions are
evaluated and values are displayed according to the current
MODE
settings.
Matrices are displayed in entry format and wrap to the next line.
text
cannot include
!
. (
PRGM I/O
item
6
)
Output(
line
,
column
,"
text
")
Output(
line
,
column
,
value
)
In
Split
screen
MODE
, the maximum value of
row
is 4 for
Output(
.
13-16 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 16 of 18
getKey
getKey
returns a number corresponding to the last key pressed, according
to the diagram below. If no key has been pressed, it returns 0.
getKey
can
be used inside loops to transfer control; for example, to create video
games. (
PRGM I/O
item
7
)
Note: You can press
É
at any time to act as a break during execution
(page 13
.
4).
Programming 13-17
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 17 of 18
ClrHome
ClrHome
(clear Home screen) clears the Home screen during execution
and places the cursor in the upper left corner, but program execution does
not pause unless
Pause
is encountered. (
PRGM I/O
item
8
)
ClrTable
ClrTable
(clear table) clears the table in the table editor during execution
and places the cursor in the upper left corner, but program execution does
not pause unless
Pause
is encountered. (
PRGM I/O
item
9
)
PrintScreen
PrintScreen
(print screen) prints the current screen on a printer attached
to an IBM
ê
-compatible computer or a Macintosh
ê
if you are using
TI-GRAPH LINK
é
software (Chapter 16). The dotted-bar pause indicator
displays. Press
Í
to resume execution.
PrintScreen
acts like
Pause
if
you are not using
TI-GRAPH LINK
. (
PRGM I/O
item
0
)
Get(
Get(
gets the contents of
variable
on another TI
.
82 and stores it to
variable
on the receiving TI
.
82.
variable
may be a number, list, list element, matrix,
matrix element,
Y=
variable, graph database or picture.
Get(
also can be
used to get data from an external compatible device. (
PRGM I/O
item
A
)
Get(
variable
)
Send(
Send(
sends the contents of
variable
to an external compatible device. It
cannot be used to send to another TI
.
82. (
PRGM I/O
item
B
)
Send(
variable
)
13-18 Programming
8213PROG.DOC TI-82, Chapter 13, English Bob Fedorisko Revised: 02/09/01 9:25 AM Printed:
02/09/01 12:42 PM Page 18 of 18
Calling Other Programs
On the TI
.
82, any program can be called from another program as a subroutine.
Enter the name of the program to use as a subroutine on a line by itself.
Calling a Program from Another Program
To call one program from another, begin on a blank line in the program
editor and do one of the following:
¦
Press
|
to display the
PRGM EXEC
menu and select the name of
the program.
prgm
and the name are copied to the current cursor
location.
¦
Select
prgm
from the
PRGM CTL
menu and then type the letters of the
program
name
(page 13
.
11).
prgm
name
When this instruction is encountered during execution, the next command
that the program executes is the first command in the second program. It
returns to the subsequent command in the first program when it encounters
either a
Return
instruction or the implied
Return
at the end.
PROGRAM:VOLCYL
⇒
PROGRAM:AREACIRC
:Prompt D
⇑
:D
à
2
!
R
:Prompt H
⇑
:
π
…
R
2
!
A
:prgmAREACIRC
⇒ ⇑
:Return
⇒
⇒
⇒
⇒
:A
…
H
!
V
⇓
⇑
:Disp V
⇓
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
⇐
Notes about Calling Programs
Variables are global.
label
used with
Goto
and
Lbl
is local to the program in which it is located.
label
in one program is not “known” by another program. You cannot use
Goto
to branch to a
label
in another program.
Return
exits a subroutine and returns to the calling program, even if
encountered within nested loops.
Applications 14-1
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 1 of 20
Chapter 14: Applications
This chapter contains application examples that incorporate features described
in the preceding chapters. Several of the examples use programs.
Chapter Contents
Left-Brain, Right-Brain Test Results
...............
14
-
2
Speeding Tickets
.............................
14
-
4
Buying a Car, Now or Later?
....................
14
-
5
Graphing Inequalities
.........................
14
-
6
Solving a System of Nonlinear Equations
...........
14
-
7
Program: Sierpinski Triangle
....................
14
-
8
Cobweb Attractors
...........................
14
-
9
Program: Guess the Coefficients
.................
14
-
10
The Unit Circle and Trigonometric Curves
..........
14
-
11
Ferris Wheel Problem
.........................
14
-
12
Reservoir Problem
...........................
14
-
14
Predator-Prey Model
..........................
14
-
16
Fundamental Theorem of Calculus
................
14
-
18
Finding the Area between Curves
.................
14
-
20
14-2 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 2 of 20
Left-Brain, Right-Brain Test Results
An experiment found a significant difference between the ability of boys and girls
to identify objects held in their left hands (which are controlled by the right side
of the brain) versus their right hands (which are controlled by the left side of the
brain). The TI Graphics team decided to conduct a similar test for adult men and
women.
Problem
30 small objects were chosen. Coworkers held half of the objects (which
they were not allowed to see) in their left hands and half in their right
hands and tried to identify them. Use box plots to compare visually the
results from the table below.
Correct Responses
Left
Right
Left
Men
Right
84712
9386
12 7 7 12
11 12 5 12
10 11 7 7
811 811
12 13 11 12
712 4 8
9111012
11 12 14 11
13 9
59
Procedure
1. Press
…
1
(to select
Edit...
). If there are values in any of the lists,
follow the procedure to clear lists described in Chapter 12. Enter the
values for the number of correct guesses each woman made with her
left hand in
L
1
.
2. Press
~
to move to
L
2
and enter the scores that each woman made with
her right hand.
3. Enter the men’s scores in
L
3
and
L
4
.
4. Press
y
ã
STAT PLOT
ä
1
(to select
Plot1
). Turn on
Plot1
and define it as
a box plot, using
L
1
. Press
y
ã
STAT PLOT
ä
2
(to select
Plot2
). Turn on
Plot2
and define it as a box plot, using
L
2
.
5. Press
o
and turn off any selected functions. Press
p
. Set
Xscl=1
,
Ymin=0
,
Yscl=0
. (Ignore the other
WINDOW
settings, which will be set
by
ZoomStat
.)
Applications 14-3
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 3 of 20
6. Press
q
9
(to select
ZoomStat
). This adjusts the viewing
WINDOW
and displays the box plots for the women’s results (left on top).
7. Press
r
and examine
minX
,
Q
1
,
Med
,
Q
3
, and
maxX
for each plot.
What is the median for the left hand? For the right hand? Does it appear
that the women guessed correctly more often with the left or right
hand?
8. Examine the men’s results. Press
y
ã
STAT PLOT
ä
and redefine
Plot1
to
use
L
3
and
Plot2
to use
L
4
. Press
r
. What difference do you see
between the plots?
9. Compare the left-hand results. Press
y
ã
STAT PLOT
ä
and redefine
Plot1
to use
L
1
and
Plot2
to use
L
3
. Press
r
. Were women or men better
at guessing with their left hands?
10. Compare the right-hand results. Press
y
ã
STAT PLOT
ä
and redefine
Plot1
to use
L
2
and
Plot2
to use
L
4
. Press
r
. Were women or men
better at guessing with their right hands?
The original experiment found that boys did not guess as well with their
right hands, while girls guessed equally well with either hand. That is
not what these box plots showed for adults. Do you think that this is
because adults have learned to adapt or because our sample was not
large enough?
14-4 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 4 of 20
Speeding Tickets
The fine for speeding in your area is 50 plus 5 per kilometer per hour over the
limit for the first 10 kilometers, plus 10 per kilometer per hour for the next 10
kilometers, plus 20 per kilometer thereafter. Graph the piecewise function that
describes the cost of the ticket in a 45-kilometer-per-hour zone.
Problem
The fine (
Y
) as a function of kilometers per hour (
X
) is:
Y = 0 0 < X
45
Y = 50 + 5 (X – 45) 45 < X
55
Y = 50 + 5
…
10 + 10 (X – 55) 55 < X
65
Y = 50 + 5
…
10 + 10
…
10 + 20 (X – 65) 65 < X
Procedure
1. Press
z
. Select
Func
,
Dot
, and the defaults. Press
y
[
STAT PLOT
]
and turn off all stat plots.
2. Press
o
. Turn off any selected functions. The
TEST
operations are
used to define piecewise functions. Enter the
Y=
function to describe
the fine.
Y
1
=(50+5(X–45))(45<X)(X
55)
+(100+10(X–55))(55<X)(X
65)
+(200+20(X–65))(65<X)
3. Press
p
and set
Xmin =
M
2
,
Xscl = 10
,
Ymin =
M
5
, and
Yscl = 10
.
Ignore
Xmax
and
Ymax
. (They are set by
@
X
and
@
Y
in step 4.)
4. Press
y
ã
QUIT
ä
to return to the Home screen and store
1
to
@
X
and
5
to
@
Y
. (
@
X
and
@
Y
, the distance between the centers of adjacent pixels,
are on the
VARS Window...
menu.) Defining
@
X
and
@
Y
as integers
produces nice values for
TRACE
.
5. Press
r
to plot the functions. At what speed does the ticket exceed
250?
Applications 14-5
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 5 of 20
Buying a Car, Now or Later?
You have identified the car you would like to buy, which costs 8,000. You can
afford payments of 250 per month. You can either borrow the money at 10%
annual interest (compounded monthly) and buy the car now, or invest the
payments at 6% and pay cash for the car later. How long will it take to pay for the
car each way?
Procedure
1. Press
z
. Select the default
MODE
settings. Press
y
[
STAT PLOT
]
and turn off all stat plots.
2. On the Home screen, store the values of the periodic interest rates.
.06
à
12
!
Z
.10
à
12
!
J
3. Press
o
. Turn off all functions and enter the formula to describe
investing the money.
Y
2
=250((1+
Z
)^X–1)
àZ
4. Enter the formula to describe making car payments.
Y
3
=8000–250(1–(1+J)^
M
X)
à
J
5. To determine how many months will be required to pay cash, press
y
ã
QUIT
ä
to return to the Home screen. Solve the equation (the amount
saved less 8000) for
X
, using 36 months as the guess. (
solve(
is on the
MATH MATH
menu.)
solve(Y
2
–8000,X,36)
6. To determine how long it will take to pay off the loan, enter:
solve(Y
3
,X,36)
7. To calculate how much you would pay in total if you got a loan, press
¯
250
, which multiplies the months to pay off the loan (in
Ans
) by the
payment amount.
8. Press
y
ã
TABLE
ä
to examine the amount saved versus the amount still
owed for each time period.
9. Press
p
. Set the viewing
WINDOW
.
Xmin = 0 Ymin = 0
Xmax = 47 Ymax = 8000
Xscl = 12 Yscl = 1000
10. Press
r
to examine the amounts graphically.
14-6 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 6 of 20
Graphing Inequalities
Examine the inequality
.
4X
3
–3X+5<
.
2X+4 graphically. Use the TEST functions to
explore the values of X where the inequality is true and where it is false.
Procedure
1. Press
z
. Select
Dot
,
Simul
, and the default
MODE
settings. Press
y
[
STAT PLOT
] and turn off all stat plots.
2. Press
o
. Turn off all functions. Enter the left side of the inequality as
Y
4
and the right side as
Y
5
.
Y
4
=.4X
3
–3X+5
Y
5
=.2X+4
3. Enter the statement of the inequality as
Y
6
. This function evaluates to 1
if true and 0 if false.
Y
6
=Y
4
<Y
5
4. Press
q
6
to graph the inequality in the standard
WINDOW
.
5. Press
r
†
†
to move to
Y
6
and trace the inequality, observing the
value of
Y
.
6. Press
o
. Turn off
Y
4
,
Y
5
, and
Y
6
. Enter equations to graph only the
inequality.
Y
7
=Y
6
Y
4
Y
8
=Y
6
Y
5
7. Press
r
. Notice that the values of
Y
7
and
Y
8
are zero where the
inequality is false.
Applications 14-7
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 7 of 20
Solving a System of Nonlinear Equations
Solve the equation X
3
–
2X=2cosX graphically. Stated another way, solve the
system of two equations and two unknowns: Y=X
3
–
2X and Y=2cosX. Use the
ZOOM factors to control the decimal places displayed on the graph.
Procedure
1. Press
z
. Select the default
MODE
settings. Press
y
[
STAT PLOT
]
and turn off all stat plots. Press
o
. Turn off all functions and enter the
functions
Y
7
=X
3
–2X
and
Y
8
=2cos X
.
2. Press
q
and select
ZDecimal
. The display shows that there are two
areas that might contain solutions (points where the two functions
appear to intersect).
3. Press
q
~
and select
SetFactors...
from the
ZOOM MEMORY
menu.
Set
XFact=10
and
YFact=10
.
4. Press
q
2
(to select
Zoom In
). Use
~
,
|
,
}
, and
†
to position the
free-moving cursor on the apparent intersection of the functions on the
right side of the display. As you move the cursor, note that the
X
and
Y
coordinates have one decimal place.
5. Press
Í
to zoom in. Move the cursor over the intersection. As you
move the cursor, note that now the
X
and
Y
coordinates have two
decimal places.
6. Press
Í
to zoom in again. Move the free-moving cursor to a point
exactly on the intersection. Note the number of decimal places.
7. Press
y
ã
CALC
ä
and select
intersect
. Press
Í
to select the
First curve
and
Í
to select the
Second curve
. Now trace to a
Guess
near the intersection and press
Í
. What are the coordinates of the
intersection?
8. Press
q
and select
ZDecimal
to redisplay the original graph.
9. Press
q
. Select
Zoom In
and explore as above the other apparent
intersection.
14-8 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 8 of 20
Program: Sierpinski Triangle
This program creates a drawing of a famous fractal, the Sierpinski Triangle, and
stores the drawing in a picture.
Program
PROGRAM:SIERPINS
:FnOff :ClrDraw
:PlotsOff
:AxesOff
:0
!
Xmin:1
!
Xmax
:0
!
Ymin:1
!
Ymax
Set viewing
WINDOW
:rand
!
X:rand
!
Y
:For(K,1,3000)
:rand
!
N
Beginning of
For
group
:If N
1
à
3
:Then
:.5X
!
X
:.5Y
!
Y
:End
If
/
Then
group
:If 1
à
3<N and N
2
à
3
:Then
:.5(.5+X)
!
X
:.5(1+Y)
!
Y
:End
If
/
Then
group
:If 2
à
3<N
:Then
:.5(1+X)
!
X
:.5Y
!
Y
:End
If
/
Then
group
:Pt-On(X,Y)
Draw point
:End
:StorePic Pic6
End of
For
group
Note: After executing this program, you can recall and display the picture
with the instruction
RecallPic Pic6
.
Applications 14-9
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 9 of 20
Cobweb Attractors
Using Web WINDOW FORMAT, you can identify points with attracting and
repelling behavior in sequence graphing.
Procedure
1. Press
z
. Select
Seq
. Press
p
~
. Select
Web
and the defaults.
Press
y
[
STAT PLOT
] and turn off all stat plots.
2. Press
o
. Enter the sequence. (
U
n
-
1
is on the keyboard.)
U
n
=KU
n
-
1
(1–U
n
-
1
)
3. Press
y
ã
QUIT
ä
to return to the Home screen and store
2.9
to
K
.
4. Press
p
. Set the
WINDOW
variables.
U
n
Start = .01 Xmin = 0 Ymin = 0
V
n
Start = 0 Xmax = 1 Ymax = 1
n
Start = 0 Xscl = 1 Yscl = 1
n
Min = 0
n
Max = 10
5. Press
r
to display the graph, and then press
~
to trace the cobweb.
This is a cobweb with one attractor.
6. Change
K
to
3.44
and
TRACE
to show a cobweb with two attractors.
7. Change
K
to
3.54
and
TRACE
to show a cobweb with four attractors.
14-10 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 10 of 20
Program: Guess the Coefficients
This program graphs the function A sin BX with random integer coefficients
between 1 and 10. You then try to guess the coefficients and graph your guess as
C sin DX. The program continues until your guess is correct.
Program
PROGRAM:GUESS
:PlotsOff :Func
:FnOff :Radian
:ClrHome
:"Asin BX"
!
Y
1
:"Csin DX"
!
Y
2
Define equations
:iPart 10rand+1
!
A
:iPart 10rand+1
!
B
:0
!
C:0
!
D
Initialize coefficients
:
-
2
p
!
Xmin
:2
p
!
Xmax
:
pà
2
!
Xscl
:
-
10
!
Ymin
:10
!
Ymax
:1
!
Yscl
Set viewing
WINDOW
:DispGraph
:Lbl Z
Display graph
:Prompt C,D
Prompt for guess
:If C=A
:Text(1,1,"C IS
OK")
:If C
ƒ
A
:Text(1,1,"C IS
WRONG")
:If D=B
:Text(1,50,"D IS
OK")
:If D
ƒ
B
:Text(1,50,"D IS
WRONG")
:DispGraph
:Pause
Display results
:If C=A and D=B
:Stop
:Goto Z
Quit if guesses are correct
Applications 14-11
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 11 of 20
The Unit Circle and Trigonometric Curves
You can use the parametric graphing feature of the TI
.
82 to show the relationship
between the unit circle and any trigonometric curve.
Problem
Graph the unit circle and the sine curve to demonstrate graphically the
relationship between them.
Any function that can be plotted in function graphing can be plotted in
parametric graphing by defining the
X
component as
T
and the
Y
component as F(
T
).
Solution
1. Press
z
. Select
Radian
,
Par
, and
Simul
.
2. Press
p
. Set the viewing
WINDOW
.
Tmin = 0 Xmin =
M
2 Ymin =
M
3
Tmax = 2
p
Xmax = 2
p
Ymax = 3
Tstep = .1 Xscl =
pà
2 Yscl = 1
3. Press
o
. Turn off all selected functions. Enter the expressions to
define the unit circle centered at (
L
1,0).
X
1T
=cos T–1
Y
1T
=sin T
4. Enter the expressions to define the sine curve.
X
2T
=T
Y
2T
=sin T
5. Press
r
. As the graph is plotting, you may press
Í
to pause and
resume graphing as you watch the sine function “unwrap” from the unit
circle.
Note: The “unwrapping” can be generalized. Replace
sin T
in
Y
2T
with any
other trig function to “unwrap” that function.
14-12 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 12 of 20
Ferris Wheel Problem
Use two pairs of parametric equations to describe two objects in motion, a
person on a ferris wheel and a ball thrown to that person. Determine when the
two objects are closest.
Problem
The ferris wheel has a diameter of 20 meters (d) and is rotating
counterclockwise at a rate of one revolution every 12 seconds (s). The
following parametric equation describes the location of the person on the
ferris wheel at time T, where
a
is the angle of rotation, the bottom center of
the ferris wheel is (0,0), and the passenger is at the rightmost point (10,10)
when T = 0.
X(T) = r cos
a
where
a
= 2
p
T
à
s and r = d
à
2
Y(T) = r + r sin
a
The ball is thrown from a height even with the bottom of the ferris wheel,
but 25 meters (b) to the right of the bottom center of the ferris wheel (25,0),
with velocity (v
0
) of 22 meters per second at an angle (
q
) of 66
¡
from the
horizontal. The following parametric equation describes the location of the
ball at time T.
X(T) = b – T v
0
cos
q
Y(T) = T v
0
sin
q
– (g
à
2) T
2
(g = 9.8 m/sec
2
)
Solution
1. Press
z
. Select
Par
,
Connected
, and
Simul
. Simultaneous
MODE
simulates what is happening with the two objects in motion over time.
2. Press
o
and turn off all functions. Press
y
[
STAT PLOT
] and turn off
all stat plots.
3. Press
p
. Set the viewing
WINDOW
.
Tmin = 0 Xmin =
M
13 Ymin = 0
Tmax = 12 Xmax = 34 Ymax = 31
Tstep = .1 Xscl = 10 Yscl = 10
4. Press
o
. Enter the expressions to define the path of the ferris wheel
and the path of the ball.
X
1T
= 10cos (
p
T
à
6)
Y
1T
= 10+10sin (
p
T
à
6)
X
2T
= 25–22Tcos 66
¡
Y
2T
= 22Tsin 66
¡
–(9.8
à
2)T
2
Applications 14-13
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 13 of 20
5. Press
s
to graph the equations and watch closely as they are
plotted. Notice that the ball and the passenger on the ferris wheel
appear to be closest near where the paths cross in the upper right
quadrant of the ferris wheel.
6. Press
p
. Change the viewing
WINDOW
to concentrate on this
portion of the graph.
Tmin = 1 Xmin = 0 Ymin = 10
Tmax = 3 Xmax = 23.5 Ymax = 25.5
Tstep = .03 Xscl = 10 Yscl = 10
7. Press
r
. After the graph is plotted, press
~
to move near the point
on the ferris wheel where the paths cross. Note the values of
X
,
Y
, and
T
.
8. Press
†
to move to the curve of the ball. Note the values of
X
and
Y
(
T
is unchanged). Notice where the cursor is located. This is the position
of the ball when the person on the ferris wheel passes the intersection.
Did the ball or the person reach the intersection first?
Using
TRACE
, you can, in effect, take “snapshots” in time to explore the
relative behavior of two objects in motion.
14-14 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 14 of 20
Reservoir Problem
On the TI
.
82, parametric graphing can be used to animate a process, providing
valuable insight into dynamic problems such as water flow out of a reservoir.
Problem
A new park has a series of waterfalls, fountains, and pools (reservoirs). The
height of one of the reservoirs is 2 meters. Several holes of relatively small
diameter will be drilled in the side to make streams of water that fall into
the next pool.
At what height on the reservoir should a hole be placed to get the
maximum distance for the water jet? (Assume that the hole is at x=0, there
is no acceleration in the x-direction, and there is no initial velocity in the
y-direction.)
Integrating the definition of acceleration in both the x and y directions
twice yields the equations x=v
0
t and y=h
0
–(g
à
2)t
2
. Solving Bernoulli’s
equation for v
0
and substituting into v
0
t, we get the parametric equations
xt = t
‡
(2 g (2 – h
0
))
yt = h
0
– (g
à
2) t
2
where t is the time in seconds, h
0
is the height of the hole in the reservoir in
meters, and g is the acceleration of gravity (9.8 meters/sec
2
).
Procedure
1. Press
z
. Select
Par
,
Simul
, and the defaults.
2. Press
o
and
‘
all functions. Enter the equations to plot the water
jet for a hole at height
0.5
meters.
X
1T
=T
‡
(2
…
9.8(2–0.50))
Y
1T
=0.50–(9.8
à
2)T
2
3. Press
Í
to move to
X
2T
. Press
y
[
RCL
]
y
[
Y-VARS
]
2
(to display
the
Parametric...
menu)
1
(to select
X
1T
)
Í
. This recalls the
contents of
X
1T
into
X
2T
. Change the height from
0.50
to
0.75
meters.
Repeat the process to recall
Y
1T
into
Y
2T
and edit it.
Applications 14-15
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 15 of 20
4. Repeat step 3 to create three more pairs of equations using the heights
1.00
,
1.50
, and
1.75
meters.
5. Press
p
. Set the viewing
WINDOW
.
Tmin = 0 Xmin = 0 Ymin = 0
Tmax =
‡
(4
à
9.8) Xmax = 2 Ymax = 2
Tstep = .01 Xscl = .5 Yscl = .5
6. Press
q
and select
ZSquare
.
ZSquare
adjusts the
WINDOW
variables to include the viewing
WINDOW
you specified, while
providing a realistic (proportional) visual representation of the water
jets. It then graphs the trajectories of the water jets from the 5 chosen
heights. What height seems to provide the maximum distance for the
water jet?
7. Use
TRACE
to determine the distance from the reservoir where each
water jet hits the next pool.
8. Where would you place the holes to construct a fountain that you find
visually interesting?
9. Can you think of a way to construct the problem to show two levels of
fountains?
14-16 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 16 of 20
Predator-Prey Model
Use sequence graphing on the TI
.
82 to explore the well-known predator-prey
model in biology. Determine the numbers of rabbits and wolves that maintain
population equilibrium in a certain region.
Problem
R = Number of rabbits.
M = Growth rate of rabbits if there are no wolves.
K = Rate at which wolves can kill rabbits.
W = Number of wolves.
G = Growth rate of wolves if there are rabbits.
D = Death rate of wolves if there are no rabbits.
R
n
=R
n
N
1
(1 + M – K W
n
N
1
)
W
n
=W
n
N
1
(1 + G R
n
N
1
– D)
Procedure
1. Press
z
. Select
Seq
and the defaults. Press
p
~
. Select
Time
FORMAT
and the defaults. Press
y
[
STAT PLOT
] and turn off all stat
plots.
2. Press
o
. Enter functions to describe the number of rabbits (
U
n
) and
the number of wolves (
V
n
) for
M = .05
,
K = .001
,
G = .0002
,
D = .03
. (
V
n
-
1
and
U
n
-
1
are
2nd
operations on the keyboard.)
U
n
=U
n
-
1
(1+.05
N
.001V
n
-
1
)
V
n
=V
n
-
1
(1+.0002U
n
-
1
N
.03)
3. Press
p
and set the initial population of rabbits (
200
) and wolves
(
50
), the number of time periods to plot (
400
), and the size of the
viewing
WINDOW
.
U
n
Start = 200 Xmin = 0 Ymin = 0
V
n
Start = 50 Xmax = 400 Ymax = 300
n
Start = 0 Xscl = 100 Yscl = 100
n
Min = 0
n
Max = 400
4. Press
r
to plot and explore the number of rabbits (
U
n
) and wolves
(
V
n
) over time (
n
). Determine the maximum and minimum number of
each.
Applications 14-17
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 17 of 20
5. Enter the program:
PROGRAM:ORBIT
:ClrDraw:FnOff
:PlotsOff :Dot
:Un(1,99,1)
!
L
1
:Vn(1,99,1)
!
L
2
:Un(100,198,1)
!
L
3
:Vn(100,198,1)
!
L
4
:Un(199,297,1)
!
L
5
:Vn(199,297,1)
!
L
6
:min(L1)
-
10
!
Xmin
:max(L1)+10
!
Xmax
:10
!
Xscl
:min(L
2
)
-
10
!
Ymin
:max(L
2
)+10
!
Ymax
:10
!
Yscl
:For(I,1,99)
:Pt-On(L
1
(I),L
2
(I))
:End
:For(I,1,99)
:Pt-On(L
3
(I),L
4
(I))
:End
:For(I,1,99)
:Pt-On(L
5
(I),L
6
(I))
:End
6. Execute
prgmORBIT
, which shows the cycle of the numbers of rabbits
(
X
axis) and wolves (
Y
axis) over 297 periods. Use the free-moving
cursor to explore the number of rabbits and wolves.
14-18 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 18 of 20
Fundamental Theorem of Calculus
The TI
.
82 can graph functions that are defined by integrals or derivatives, using
the functions fnInt( and nDeriv( from the MATH MATH menu.
Problem 1
Demonstrate graphically that
F(x) =
‰
1
x
1
à
t dt = ln(x), x>0 and that
D
x
[
‰
1
x
1
à
t dt ] = 1
à
x
Procedure 1
1. Press
z
. Select
Simul
and the default
MODE
settings. Press
o
and
turn off all functions. Press
y
[
STAT PLOT
] and turn off all stat plots.
2. Press
p
. Set the viewing
WINDOW
.
Xmin = .01 Ymin =
M
1.5
Xmax = 10 Ymax = 2.5
Xscl = 1 Yscl = 1
3. Press
o
. Enter the numerical integral of 1
à
T and the mathematical
integral of 1
à
X.
Y
1
=fnInt(1
à
T,T,1,X)
Y
2
=ln X
4. Press
r
. The busy indicator displays while the graph is being
plotted. Use the cursor keys to compare the values of
Y
1
and
Y
2
.
5. Press
o
. Turn off
Y
1
and
Y
2
, and then enter the numerical derivative of
the integral of 1
à
X and the function 1
à
X.
Y
3
=nDeriv(Y
1
,X,X)
Y
4
=1
à
X
6. Press
r
. The busy indicator displays while the graph is being
plotted. Again, use the cursor keys to compare the values of the two
graphed functions,
Y
3
and
Y
4
.
Applications 14-19
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 19 of 20
Problem 2
Explore the functions defined by
y =
‰
.
2
x
t
2
dt,
‰
0
x
t
2
dt, and
‰
2
x
t
2
dt
Procedure 2
1. Press
o
. Turn off all functions. On the TI
.
82, the three functions above
can be defined simultaneously using a list.
Y
5
=fnInt(T
2
,T,{
M
2,0,2},X)
2. Press
z
. Select
Sequential
.
3. Press
q
6
to select
ZStandard
.
4. Press
r
. Notice that the functions appear identical, but shifted
vertically by a constant.
5. Press
o
. Enter the numerical derivative of
Y
5
.
Y
6
=nDeriv(Y
5
,X,X)
6. Press
r
. Notice that although the three graphs defined by
Y
5
are
unique, they share the same derivative.
14-20 Applications
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 20 of 20
Finding the Area between Curves
Find the area of the region bounded by:
f(x) = 300 x
à
(x
2
+ 625)
g(x) = 3 cos
.
1 x
x = 75
Procedure
1. Press
z
. Select the default
MODE
settings. Press
o
and turn off all
functions. Press
y
[
STAT PLOT
] and turn off all stat plots.
2. Press
p
. Set the viewing
WINDOW
.
Xmin = 0 Ymin =
M
5
Xmax = 100 Ymax = 10
Xscl = 10 Yscl = 1
3. Press
o
. Enter the upper and lower functions.
Y
1
=300X
à
(X
2
+625)
Y
2
=3cos .1X
4. Press
y
ã
CALC
ä
and select
intersection
. The graph is displayed. Select
First curve
,
Second curve
, and
Guess
for the intersection at the left of
the display. The solution is displayed, and the value of
X
at the
intersection, which is the lower limit of the integral, is stored in
Ans
and
X
.
5. Press
y
ã
DRAW
ä
and use
Shade(
to see the area graphically.
Shade(Y
2
,Y
1
,1,Ans,75)
6. Press
y
ã
QUIT
ä
to return to the Home screen. Enter the expression to
evaluate the integral for the shaded region.
fnInt(Y
1
–Y
2
,X,Ans,75)
The area is
325.839962
.
Memory Management 15-1
8215MEM.DOC TI-82, Chapter 15, English Bob Fedorisko Revised: 02/09/01 9:28 AM Printed: 02/09/01
12:43 PM Page 1 of 4
Chapter 15: Memory Management
This chapter describes how to manage memory on the TI
.
82. To increase the
amount of memory available for use, occasionally you may want to delete from
memory items that you are no longer using. You also can reset the calculator,
erasing all data and programs.
Chapter Contents
Checking Available Memory
.....................
15-2
Deleting Items from Memory
....................
15-3
Resetting the TI
.
82
...........................
15-4
15-2 Memory Management
8215MEM.DOC TI-82, Chapter 15, English Bob Fedorisko Revised: 02/09/01 9:28 AM Printed: 02/09/01
12:43 PM Page 2 of 4
Checking Available Memory
The MEMORY Check RAM screen displays the total amount of available memory
and the amount of memory used by each variable type. This allows you to
determine the amount of memory available for new items such as programs and
the amount used by old items that you no longer need.
Displaying the MEM FREE Screen
1. Press
y
ã
MEM
ä
to display the
MEMORY
screen.
2. Select
Check RAM...
.
The number of bytes used by each variable type is shown on the right.
3. To leave the
Check RAM
display:
¦
To go to the Home screen, press
y
ã
QUIT
ä
.
¦
To return to the
MEMORY
screen, press
y
ã
MEM
ä
.
Memory Management 15-3
8215MEM.DOC TI-82, Chapter 15, English Bob Fedorisko Revised: 02/09/01 9:28 AM Printed: 02/09/01
12:43 PM Page 3 of 4
Deleting Items from Memory
You can delete the contents of any variable (real number, list, matrix, Y=
function), program, picture, or graph database from memory to increase available
memory.
Deleting an Item
1. Press
y
ã
MEM
ä
to display the
MEMORY
screen.
2. Select
Delete...
.
3. Select the type of item that you want to delete. (If you select
All...
, a list
of all items is displayed.) A screen appears listing all variables of that
type and the amount used by each.
For example, if you select
List...
, the
DELETE:List
screen appears.
4. Use
}
and
†
to position the cursor, which is indicated by
4
in the left
column, next to the item you want to delete, and press
Í
. The item
is deleted immediately.
You can continue to delete individual items from this screen. To leave the
DELETE
display:
¦
To go to the Home screen, press
y
ã
QUIT
ä
.
¦
To return to the
MEMORY
screen, press
y
ã
MEM
ä
.
Note: Some system variables can’t be deleted; for example,
Ans
and
statistical variables such
RegEQ
.
15-4 Memory Management
8215MEM.DOC TI-82, Chapter 15, English Bob Fedorisko Revised: 02/09/01 9:28 AM Printed: 02/09/01
12:43 PM Page 4 of 4
Resetting the TI-82
Resetting the TI
.
82 restores memory to the factory settings, including deleting
the contents of all variables and programs and resetting all system variables to
the original settings. Because you can increase available memory by deleting
individual items, you should rarely need to reset the TI
.
82.
Resetting
1. Press
y
ã
MEM
ä
to display the
MEMORY
screen.
2. Select
Reset...
.
3. Make the appropriate menu selection:
¦
To go to the Home screen without resetting memory, select
No
.
¦
To reset memory, select
Yes
. The Home screen is displayed with the
message
Mem cleared
.
Note:
Reset
resets the contrast to the factory setting. If the screen is blank,
you need to adjust the display contrast. Press
y
and then press and hold
}
(to make the display darker) or
†
(to make the display lighter). You can
press
‘
to clear the message on the display.
Communication Link 16-1
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 1 of 8
Chapter 16: Communication Link
The TI
.
82 has a port to let you communicate with another TI
.
82, with a
compatible device such as a CBL 2
é
/CBL
é
or CBR
é
, or with a PC or
Macintosh
ë
. This chapter describes how to communicate with another TI
.
82.
Chapter Contents
Getting Started: Sending Variables
................
16-2
TI
.
82
LINK
..................................
16-3
Selecting Items
..............................
16-4
Transmitting Items
...........................
16-6
Receiving Items
.............................
16-7
Backing Up Memory
..........................
16-8
16-2 Communication Link
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 2 of 8
Getting Started: Sending Variables
Getting Started is a fast-paced introduction. Read the chapter for details.
Create and store a variable and a random matrix and then transfer them to
another TI
.
82.
1. On the Home screen, press
5
¥
3
¿
ƒ
Q
Í
.
2. Press
~
6
(to select
randM(
). Press
3
¢
3
¤
¿
1
(to select
ã
A
ä
)
Í
to store a
random matrix into
ã
A
ä
.
3. Connect the calculators together with the cable.
4. On the receiving unit, press
y
ã
LINK
ä
~
to
display the
RECEIVE
menu. Press
1
(to select
Receive
). The message
Waiting...
is displayed.
5. On the sending unit, press
y
ã
LINK
ä
to display
the
SEND
menu. Press
2
to select
SelectAll–
and
display the
SELECT
screen with no items
selected.
6. Press
†
until the cursor is on the line with
ã
A
ä
.
Press
Í
. The square dot indicates that
ã
A
ä
is
selected to send.
7. Press
†
until the cursor is on the line with
Q
.
Press
Í
to select
Q
also.
8. On the sending unit, press
~
to place the cursor
on
TRANSMIT
.
9. Press
1
(to select
Transmit
) and begin
transmission. The items are transmitted and
both units display the names and types of the
transmitted variables.
Communication Link 16-3
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 3 of 8
TI-82 LINK
The TI
.
82 communication capability lets you share variables and programs or
entire memory backup with another TI
.
82 or with a personal computer. You can
print TI
.
82 screens on a printer connected to a computer.
Linking to Another TI-82
The software for one TI
.
82 to communicate with another is built into the
TI
.
82. The instructions are in this chapter.
Note: You cannot transmit items between the TI
.
82 and the TI
.
85 or TI
.
86.
You can transmit some items between the TI
.
82 and the TI
.
83. See the
TI
.
83 Guidebook
for more information.
Linking to a CBL 2/CBL or CBR
The CBL 2
é
/CBL
é
(Calculator-Based Laboratory
é
) System and CBR
é
(Calculator-Based Ranger
é
) are optional accessories that connect to the
TI
.
82
LINK
port and are used to collect and analyze real-world data.
Linking to a PC or Macintosh
An optional accessory,
TI-GRAPH LINK
é
, allows a TI
.
82 to communicate
with a personal computer.
Connecting the Cable
1. Insert either end of the cable into the port very firmly.
2. Repeat with the other TI
.
82.
Leaving a LINK Screen or Menu
To leave
LINK
:
¦
While transmitting, press
É
to interrupt and then
Quit
to leave the
ERROR
screen.
¦
After transmitting, press
y
ã
QUIT
ä
.
16-4 Communication Link
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 4 of 8
Selecting Items
You can send individual items (variables), all items, or a memory backup from
one TI
.
82 to another. To transmit from the TI
.
82, you first select what you want to
send. The transmission does not begin until you select from the TRANSMIT
menu.
What You Can Send
You may transmit:
¦
Programs
¦
Graph databases
¦
Pictures
¦
Lists
¦
Matrices
¦
Y=
functions
¦
Window settings (sent as a group)
¦
RclWindow
settings (sent as a group)
¦
Table settings (sent as a group)
¦
Real variables
Communication Link 16-5
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 5 of 8
Selecting Items to Send
1. Press
y
ã
LINK
ä
to display the
LINK SEND
menu.
2. For convenience, you can display the individual items with all of them
selected, none of them selected, or the ones from the last transmission
selected.
¦
SelectAll+
displays with all items selected.
¦
SelectAll–
displays with no items selected.
¦
SelectCurrent
reselects all currently selected items (page 16
.
6).
The
SELECT
screen is displayed where you may continue to select or
deselect individual items. Selected names are marked with a
0
.
3.
8
at the left of an item indicates the selection cursor. Use
†
and
}
to
move the cursor.
Press
Í
to reverse the selection status of the item where the cursor
is located.
16-6 Communication Link
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 6 of 8
Transmitting Items
Once you have selected what to send and the receiving unit is ready, you can
begin transmitting. For easy distribution of items to several TI
.
82 units, current
items remain selected in both the sending and receiving unit. It is easy to
transmit the items again.
Transmitting Items
After you have selected the items you want to send, press
~
to move the
cursor to
TRANSMIT
and display the
TRANSMIT
menu.
Be sure that the receiving unit is set to
Receive
(page 16
.
7). Press
Í
to
select
Transmit
.
The name and type of each item is displayed, one per line, as the TI
.
82 tries
to transmit it. After transmission is complete for all items,
Done
is
displayed. Press
}
and
†
to scroll through the names.
Transmitting Items to an Additional TI-82
After sending or receiving data, you can repeat the same transmission to a
different TI
.
82 from either the sending unit or the receiving unit without
selecting what to send. The current items remain selected.
Before you make another selection, simply connect the unit to another
TI
.
82, select
Receive
on the new unit, and then press
y
ã
LINK
ä
3
(to select
SelectCurrent...
)
~
1
(to select
Transmit
).
Error Conditions
A transmission error occurs after one or two seconds if:
¦
There is not a cable attached to the sending unit.
¦
There is not a receiving unit attached to the cable.
¦
The receiving unit is not in
Receive
mode.
Note: If the cable is attached, push it in more firmly and try again.
If the
É
key is pressed to interrupt transmission, an
ERROR
screen is
displayed. Select
Exit
to leave the
ERROR
screen.
Communication Link 16-7
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 7 of 8
Receiving Items
Items are not transmitted until the receiving unit is ready. If the receiving unit
already has a variable with that name, you have the opportunity to overwrite it,
skip it, or save it to a new name.
Receiving Unit
When you select
Receive
from the
LINK RECEIVE
menu, the busy indicator
and the message
Waiting...
is displayed and the receiving unit is ready to
receive transmitted items.
The receiving unit displays the name and type of each item as it is
accepted. After transmission is complete for all items, the message
Done
is
displayed. Press
}
and
†
to scroll through the names. The unit is not in
Receive
mode; select
Receive
to receive new items.
To leave
Receive
mode without receiving items, press
É
. Select
Quit
to
leave the
ERROR
screen.
Duplicate Name
If an item of that name exists in the receiving unit, the receiving unit
displays the
DuplicateName
menu.
¦
To store the item to a different name, select
Rename
. After the
Name=
on the prompt line, enter a variable name that is not being used in the
receiving unit (the keyboard is in
ALPHA-LOCK
). Press
Í
.
Transmission resumes.
¦
To overwrite the existing item, select
Overwrite
. Transmission resumes.
¦
To skip this item (not copy it to the receiving unit), select
Omit
.
Transmission resumes with the next item.
¦
To leave
Receive
mode, select
Quit
.
Insufficient Memory in Receiving Unit
If the receiving unit does not have sufficient memory to receive the item,
the receiving unit displays the
Memory Full
menu.
¦
To skip this item, select
Omit
. Transmission resumes with the next
item.
¦
To leave
Receive
mode, select
Quit
.
16-8 Communication Link
8216LINK.DOC TI-82 Parcus, Chapter 16, English Bob Fedorisko Revised: 02/09/01 9:33 AM Printed:
02/09/01 12:43 PM Page 8 of 8
Backing Up Memory
Backup transmits all items in memory to the receiving unit.
Memory Backup
To copy the exact contents of memory in the sending unit to the memory of
the receiving unit, put the other unit in
Receive
mode and select
Backup
from the
LINK
menu.
¦
Select
Transmit
to begin transmission.
¦
Warning:
Backup
overwrites the memory in the receiving unit and all
information in the memory of the receiving unit is lost. If you do not
want to do a backup, select
Quit
to return to the
LINK
menu.
Receiving Unit
As a safety check to prevent accidental loss of memory, when the receiving
unit receives notice of a backup, the message
WARNING Memory Backup
is
displayed.
¦
To continue with the backup process, select
Continue
. The
transmission will begin.
¦
To prevent the backup, select
Quit
.
Note: If a transmission error occurs during a backup, the receiving unit is
reset.
Tables A-1
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 1 of 28
Appendix A: Tables
This appendix provides a list of all the TI
.
82 functions that you can use in
expressions and all the TI
.
82 instructions that you can use on the Home screen
and in programs.
Appendix Contents
Table of Functions and Instructions
...............
A-2
Menu Map
.................................
A-22
Table of Variables
............................
A-28
A-2 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 2 of 28
Table of Functions and Instructions
Functions (F) return a value, list, or matrix and can be used in an expression;
instructions (I) initiate an action. Some, but not all, have arguments.
† indicates
that the instruction is available only in the program editor.
abs
value
Returns absolute value of
value
.
(F)
y
ã
ABS
ä
2
.
4
abs
list
Returns absolute value of
list
elements.
(F)
y
ã
ABS
ä
2
.
4
abs
matrix
Returns matrix of
absolute values of
matrix
elements.
(F)
y
ã
ABS
ä
10
.
10
A
ddition:
valueA
+
valueB
Returns
valueA
plus
valueB
.
(F)
Ã
2
.
3
A
ddition:
value
+
list
Returns list in which
value
is added to each
list
element.
(F)
Ã
2
.
3
A
ddition:
listA
+
listB
Returns
listA
elements
plus
listB
elements.
(F)
Ã
2
.
3
A
ddition:
matrixA
+
matrixB
Returns
matrixA
elements plus
matrixB
elements.
(F)
Ã
10
.
10
valueA
and
valueB
Returns 1 if both
valueA
and
valueB
are
ƒ
0
.
(F)
y
ã
TEST
ä
LOGIC
á
and
â
2
.
16
augment(
matrixA
,
matrixB
)
Returns
matrixA
augmented by
matrixB
.
(F)
MATH
á
augment(
â
10
.
14
AxesOff
Sets axis
FORMAT
off.
(I)
†
p
FORMAT
á
AxesOff
â
3
.
10
AxesOn
Sets axis
FORMAT
on.
(I)
†
p
FORMAT
á
AxesOn
â
3
.
10
Circle(
X
,
Y
,
radius
)
Draws a circle of center
(
X
,
Y
) and
radius
.
(I)
y
ã
DRAW
ä
DRAW
á
Circle(
â
8
.
9
ClrDraw
Deletes all drawn
elements from a graph or
drawing.
(I)
y
ã
DRAW
ä
DRAW
á
ClrDraw
â
8
.
16
Tables A-3
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 3 of 28
ClrHome
Clears the Home screen.
(I)
†
I/O
á
ClrHome
â
13
.
17
ClrList
listA
,
listB
,
. . . Clears all values from
listA
,
listB
, . . .
(I)
…
EDIT
á
ClrList
â
12
.
12
ClrTable
Clears all values from
table.
(I)
†
I/O
á
ClrTable
â
13
.
17
Connected
Sets connected line
graphing format.
(I)
†
z
á
Connected
â
1
.
11
CoordOff
Does not display cursor
coordinate values.
(I)
†
p
FORMAT
á
CoordOff
â
3
.
10
CoordOn
Displays cursor
coordinate values.
(I)
†
p
FORMAT
á
CoordOn
â
3
.
10
cos
value
Returns cosine of
value
.
(F)
™
2
.
3
cos
list
Returns cosine of
list
elements.
(F)
™
2
.
3
cos
M
1
value
Returns arccosine of
value
.
(F)
y
ã
cos
.
1
ä
2
.
3
cos
M
1
list
Returns arccosine of
list
elements.
(F)
y
ã
cos
.
1
ä
2
.
3
cosh
value
Returns hyperbolic cosine
of
value
.
(F)
HYP
á
cosh
â
2
.
11
cosh
list
Returns hyperbolic cosine
of
list
elements.
(F)
HYP
á
cosh
â
2
.
11
cosh
M
1
value
Returns hyperbolic
arccosine of
value
.
(F)
HYP
á
cosh
.
1
â
2
.
11
cosh
M
1
list
Returns hyperbolic
arccosine of
list
elements.
(F)
HYP
á
cosh
.
1
â
2
.
11
Cube:
value
3
Returns cube of
value
.
(F)
MATH
á
3
â
2
.
6
Cube:
list
3
Returns cube of
list
elements.
(F)
MATH
á
3
â
2
.
6
Cube:
matrix
3
Returns
matrix
cubed.
(I)
MATH
á
3
â
10
.
11
Cube root:
3
‡
value
Returns cube root of
value
.
(F)
MATH
á
3
‡â
2
.
6
Cube root:
3
‡
list
Returns cube root of
list
elements.
(F)
MATH
á
3
‡â
2
.
6
A-4 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 4 of 28
CubicReg
Fits data to cubic model
using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
CubicReg
â
12
.
15
CubicReg
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
cubic model.
(I)
…
CALC
á
CubicReg
â
12
.
15
CubicReg
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
cubic model with
frequency
Flist
.
(I)
…
CALC
á
CubicReg
â
12
.
15
value
8
Dec
Displays
value
as decimal.
(I)
MATH
á
8
Dec
â
2
.
5
list
8
Dec
Displays
list
as decimal.
(I)
MATH
á
8
Dec
â
2
.
5
matrix
8
Dec
Displays
matrix
as
decimal.
(I)
MATH
á
8
Dec
â
2
.
5
Degree
Sets degree
MODE
.
(I)
†
z
á
Degree
â
1
.
11
Degree notation:
angle
¡
Interprets
angle
as
degrees.
(F)
y
ã
ANGLE
ä
á
¡
â
2
.
13
DependAsk
Sets table without
dependent variables.
(I)
†
y
ã
TblSet
ä
á
DependAsk
â
7
.
5
DependAuto
Sets table to generate
dependent variables.
(I)
†
y
ã
TblSet
ä
á
DependAuto
â
7
.
5
det
matrix
Returns determinant of
matrix
.
(F)
MATH
á
det
â
10
.
12
dim
list
Returns length of
list
.
(F)
y
ã
LIST
ä
OPS
á
dim
â
11
.
7
dim
matrix
Returns dimensions of
matrix
as a list.
(F)
MATH
á
dim
â
10
.
12,13
length
!
dim
listname
Creates (if necessary) or
redimensions
list
to
length
.
(I)
y
ã
LIST
ä
OPS
á
dim
â
11
.
7
{
row
,
col
}
!
dim
matrixname
Creates (if necessary) or
redimensions
matrix
to
row
×
col
.
(I)
MATH
á
dim
â
10
.
13
Disp
Displays Home screen.
(I)
†
I/O
á
Disp
â
13
.
14
Disp
valueA
,
valueB
,
. . .
Displays
valueA
,
valueB,
. . .
(I)
†
I/O
á
Disp
â
13
.
14
DispGraph
Displays graph.
(I)
†
I/O
á
DispGraph
â
13
.
15
DispTable
Displays table.
(I)
†
I/O
á
DispTable
â
13
.
15
Tables A-5
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 5 of 28
Division:
valueA
à
valueB
Returns
valueA
divided by
valueB
.
(F)
¥
2
.
3
Division:
list
à
value
Returns
list
elements
divided by
value
.
(F)
¥
2
.
3
Division:
value
à
list
Returns
value
divided by
list
elements.
(F)
¥
2
.
3
Division:
listA
à
listB
Returns
listA
elements
divided by
listB
elements.
(F)
¥
2
.
3
answer
8
DMS
Displays
answer
in DMS
format.
(I)
y
ã
ANGLE
ä
á
8
DMS
â
2
.
14
Dot
Sets dot graphing format.
(I)
†
z
á
Dot
â
1
.
11
DrawF
expression
Draws
expression
(in
X
)
on current graph.
(I)
y
ã
DRAW
ä
DRAW
á
DrawF
â
8
.
7
DrawInv
expression
Draws inverse of
expression
(in
X
) on
current
Func
MODE
graph.
(I)
y
ã
DRAW
ä
DRAW
á
DrawInv
â
8
.
7
DS<(
variable
,
value
)
:
commandA
:
commands
Decrements
variable
by 1,
skips
commandA
if
variable
<
value
.
(I)
†
CTL
á
DS<(
â
13
.
10
e^
power
Returns e raised to
power
.
(F)
y
ã
e
x
ä
2
.
4
e^
list
Returns a list of e raised
to
list
elements.
(F)
y
ã
e
x
ä
2
.
4
Else
See
If:Then:Else
End
Indentifies end of
While
,
For
,
Repeat
, or
If
-
Then
-
Else
loop.
(I)
†
CTL
á
End
â
13
.
9
Eng
Sets engineering display
MODE
.
(I)
†
z
á
Eng
â
1
.
10
Equal:
valueA
=
valueB
Returns 1 if
valueA
=
valueB
. Returns 0 if
valueA ƒ
valueB
.
(F)
y
ã
TEST
ä
TEST
á
=
â
2
.
15
Equal:
listA
=
listB
Returns 1 if every element
of
listA
=
listB
. Returns 0
if any element of
listA ƒ
listB
.
(F)
y
ã
TEST
ä
TEST
á
=
â
2
.
15
Equal:
matrixA
=
matrixB
Returns 1 if every element
of
matrixA
=
matrixB
.
Returns 0 if any element
of
matrixA ƒ
matrixB
.
(F)
y
ã
TEST
ä
TEST
á
=
â
10
.
11
A-6 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 6 of 28
Exponent:
value
E
exponent
Returns
value
times 10 to
the
exponent
.
(F)
y
ã
EE
ä
1
.
7
Exponent:
list
E
exponent
Returns
list
elements time
10 to the
exponent
.
(F)
y
ã
EE
ä
1
.
7
Exponent:
matrix
E
exponent
Returns
matrix
elements
times 10 to the
exponent
.
(F)
y
ã
EE
ä
1
.
7
ExpReg
Fits data to exponential
model using lists from
SET UP CALCS
.
(I)
…
CALC
á
ExpReg
â
12
.
16
ExpReg
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
exponential model.
(I)
…
CALC
á
ExpReg
â
12
.
16
ExpReg
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
exponential model with
frequency
Flist
.
(I)
…
CALC
á
ExpReg
â
12
.
16
Factorial:
value
!
Returns factorial of
value
(0
integer
69).
(F)
PRB
á
!
â
2
.
12
Factorial:
list
!
Returns factorial of
list
elements.
(F)
PRB
á
!
â
2
.
12
Fill(
value
,
matrixname
)
Stores
value
to each
element in
matrixname
.
(I)
MATH
á
Fill(
â
10
.
13
Fill(
value
,
listname
)
Stores
value
to each
element in
listname
.
(I)
y
ã
LIST
ä
OPS
á
Fill(
â
11
.
8
Fix
#
Sets fixed display
MODE
for
#
decimal places.
(I)
†
z
á
#
â
1
.
10
Float
Sets floating display
MODE
.
(I)
†
z
á
Float
â
1
.
10
fMax(
expression
,
variable
,
lower
,
upper
)
Returns value of
variable
where maximum of
expression
occurs,
between
lower
and
upper
.
Tolerance is 1
E
L
5.
(F)
MATH
á
fMax(
â
2
.
6
fMax(
expression
,
variable
,
lower
,
upper
,
tolerance
)
Returns value of
variable
where maximum of
expression
occurs,
between
lower
and
upper
,
with specified
tolerance
.
(F)
MATH
á
fMax(
â
2
.
6
Tables A-7
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 7 of 28
fMin(
expression
,
variable
,
lower
,
upper
)
Returns value of
variable
where minimum of
expression
occurs,
between
lower
and
upper
.
Tolerance is 1
E
L
5.
(F)
MATH
á
fMin(
â
2
.
6
fMin(
expression
,
variable
,
lower
,
upper
,
tolerance
)
Returns value of
variable
where minimum of
expression
occurs,
between
lower
and
upper
,
with specified
tolerance
.
(F)
MATH
á
fMin(
â
2
.
6
fnInt(
expression
,
variable
,
lower
,
upper
)
Returns function integral
of
expression
with
respect to
variable
,
between
lower
and
upper
.
Tolerance is 1
E
L
5.
(F)
MATH
á
fnInt(
â
2
.
7
fnInt(
expression
,
variable
,
lower
,
upper
,
tolerance
)
Returns function integral
of
expression
with
respect to
variable
,
between
lower
and
upper
,
with specified
tolerance
.
(F)
MATH
á
fnInt(
â
2
.
7
FnOff
Deselects all Y= functions.
(I)
y
ã
Y
.
VARS
ä
ON/OFF
á
FnOff
â
3
.
7
FnOff
funcA
,
funcB
,
. . . Deselects
funcA
,
funcB
,
. . .
(I)
y
ã
Y
.
VARS
ä
ON/OFF
á
FnOff
â
3
.
7
FnOn
Selects all Y= functions.
(I)
y
ã
Y
.
VARS
ä
ON/OFF
á
FnOn
â
3
.
7
FnOn
funcA
,
funcB
,
. . . Selects
funcA
,
funcB
, . . .
(I)
y
ã
Y
.
VARS
ä
ON/OFF
á
FnOn
â
3
.
7
For(
variable
,
begin
,
end
)
:
commands . . .
:End
Executes
commands
through
End
,
incrementing
variable
from
begin
by 1 until
variable
>
end
.
(I)
†
CTL
á
For(
â
13
.
8
For(
variable
,
begin
,
end
,
increment
)
:
commands . . .
:End
Executes
commands
through
End
,
incrementing
variable
from
begin
by
increment
until
variable
>
end
.
(I)
†
CTL
á
For(
â
13
.
8
fPart
value
Returns fractional part of
value
.
(F)
NUM
á
fPart
â
2
.
9
fPart
list
Returns fractional part of
each
list
element.
(F)
NUM
á
fPart
â
2
.
9
A-8 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 8 of 28
fPart
matrix
Returns fractional part of
each
matrix
element.
(F)
NUM
á
fPart
â
10
.
11
value
8
Frac
Displays
value
as most
simplified fraction.
(I)
MATH
á
8
Frac
â
2
.
5
list
8
Frac
Displays
list
elements as
most simplified fractions.
(I)
MATH
á
8
Frac
â
11
.
2
matrix
8
Frac
Displays
matrix
elements
as most simplified
fractions.
(I)
MATH
á
8
Frac
â
2
.
5
FullScreen
Sets display
MODE
to
show full screen.
(I)
†
z
á
FullScreen
â
1
.
11
Func
Sets function graphing
MODE
.
(I)
†
z
á
Func
â
1
.
11
Get(
variable
)
Gets contents of
variable
from external device and
stores in
variable
.
(I)
†
I/O
á
Get(
â
13
.
17
getKey
Returns value of last
keystroke.
(F)
†
I/O
á
getKey
â
13
.
16
Goto
label
Transfers control to
label
.
(I)
†
CTL
á
Goto
â
13
.
10
Greater than:
valueA
>
valueB
Returns 1 if
valueA
>
valueB
. Returns 0 if
valueA
valueB
.
(F)
y
ã
TEST
ä
TEST
á
>
â
2
.
15
Greater than:
listA
>
listB
Returns 1 if
listA
element
>
listB
element.
Otherwise returns 0.
(F)
y
ã
TEST
ä
TEST
á
>
â
2
.
15
Greater than or equal:
valueA
‚
valueB
Returns 1 if
valueA
‚
valueB
. Returns 0 if
valueA
<
valueB
.
(F)
y
ã
TEST
ä
TEST
á
‚
â
2
.
15
Greater than or equal:
listA
‚
listB
Returns 1 if
listA
element
‚ listB
element.
Otherwise returns 0.
(F)
y
ã
TEST
ä
TEST
á
‚
â
2
.
15
GridOff
Sets grid
FORMAT
off.
(I)
†
p
FORMAT
á
GridOff
â
3
.
10
GridOn
Sets grid
FORMAT
on.
(I)
†
p
FORMAT
á
GridOn
â
3
.
10
Horizontal
Y
Draws horizontal line at
Y
.
(I)
y
ã
DRAW
ä
DRAW
á
Horizontal
â
8
.
5
identity
dim
Returns identity matrix
dim
×
dim
.
(F)
MATH
á
identity
â
10
.
13
Tables A-9
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 9 of 28
If
condition
:
commandA
:
commands
If
condition
= 0 (false),
skips
commandA
.
(I)
†
CTL
á
If
â
13
.
7
If
condition
:Then:
commands
:End
Executes
commands
from
Then
to
End
if
condition
= 1 (true).
(I)
†
CTL
á
Then
â
13
.
8
If
condition
:Then:
commands
:Else:
commands
:End
Executes
commands
from
Then
to
Else
if
condition
= 1 (true); from
Else
to
End
if
condition
= 0
(false).
(I)
†
CTL
á
Else
â
13
.
8
IndpntAsk
Sets table without
independent values.
(I)
†
y
ã
TblSet
ä
á
IndpntAsk
â
7
.
5
IndpntAuto
Sets table to generate
independent values.
(I)
†
y
ã
TblSet
ä
á
IndpntAuto
â
7
.
5
Input
Displays graph.
(I)
†
I/O
á
Input
â
13
.
13
Input
variable
Prompts for value to store
to
variable
.
(I)
†
I/O
á
Input
â
13
.
13
Input
"
string
",
variable
Displays
string
and stores
entered value to
variable
.
(I)
†
I/O
á
Input
â
13
.
13
int
value
Returns largest integer
value
.
(F)
NUM
á
int
â
2
.
10
int
list
Returns largest integer
list
element.
(F)
NUM
á
int
â
2
.
10
int
matrix
Returns matrix of largest
integers
each element of
matrix
.
(F)
NUM
á
int
â
10
.
11
Inverse:
value
M
1
Returns 1 divided by
value
.
(F)
—
2
.
3
Inverse:
list
M
1
Returns 1 divided by
list
elements.
(F)
—
2
.
3
Inverse:
matrix
M
1
Returns
matrix
inverted.
(F)
—
10
.
11
iPart
value
Returns integer part of
value
.
(F)
NUM
á
iPart
â
2
.
9
iPart
list
Returns integer part of
list
element.
(F)
NUM
á
iPart
â
2
.
9
iPart
matrix
Returns matrix of integer
part of each element of
matrix
.
(F)
NUM
á
iPart
â
10
.
11
IS>(
variable
,
value
)
:
commandA
:
commands
Increments
variable
by 1,
skips
commandA
if
variable
>
value
.
(I)
†
CTL
á
IS>(
â
13
.
10
A-10 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 10 of 28
LabelOff
Sets axis label
FORMAT
off.
(I)
†
p
FORMAT
á
LabelOff
â
3
.
10
LabelOn
Sets axis label
FORMAT
on.
(I)
†
p
FORMAT
á
LabelOn
â
3
.
10
Lbl
label
Assigns
label
to the
command.
(I)
†
CTL
á
Lbl
â
13
.
10
Less than:
valueA
<
valueB
Returns 1 if
valueA
<
valueB
. Returns 0 if
valueA ‚
valueB
.
(F)
y
ã
TEST
ä
TEST
á
<
â
2
.
15
Less than:
listA
<
listB
Returns 1 if
listA
element
<
listB
element; otherwise
returns 0.
(F)
y
ã
TEST
ä
TEST
á
<
â
2
.
15
Less than or equal:
valueAvalueB
Returns 1 if
valueA
valueB
. Returns 0 if
valueA
>
valueB
.
(F)
y
ã
TEST
ä
TEST
á
â
2
.
15
Less than or equal:
listAlistB
Returns 1 if
listA
element
listB
element.
Otherwise returns 0.
(F)
y
ã
TEST
ä
TEST
á
â
2
.
15
Line(
X
1
,
Y
1
,
X
2
,
Y
2
)
Draws line from (
X
1
,
Y
1
) to
(
X
2
,
Y
2
).
(I)
y
ã
DRAW
ä
DRAW
á
Line(
â
8
.
4
Line(
X
1
,
Y
1
,
X
2
,
Y
2
,0)
Erases line from (
X
1
,
Y
1
)
to (
X
2
,
Y
2
).
(I)
y
ã
DRAW
ä
DRAW
á
Line(
â
8
.
4
LinReg(a+bx)
LinReg(ax+b)
Fits data to linear model
using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
LinReg(a+bx)
â
12
.
15
á
LinReg(ax+b)
â
12
.
16
LinReg(a+bx)
Xlist
,
Ylist
LinReg(ax+b)
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
linear model.
(I)
…
CALC
á
LinReg(a+bx)
â
12
.
15
…
CALC
á
LinReg(ax+b)
â
12
.
16
LinReg(a+bx)
Xlist
,
Ylist
,
Flist
LinReg(ax+b)
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
linear model with
frequency
Flist
.
(I)
…
CALC
á
LinReg(a+bx)
â
12
.
15
…
CALC
á
LinReg(ax+b)
â
12
.
16
ln
value
Returns natural logarithm
of
value
.
(F)
µ
2
.
4
ln
list
Returns natural logarithm
of
list
elements.
(F)
µ
2
.
4
LnReg
Fits data to logarithmic
model using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
LnReg
â
12
.
16
LnReg
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
logarithmic model.
(I)
…
CALC
á
LnReg
â
12
.
16
Tables A-11
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 11 of 28
LnReg
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
logarithmic model with
frequency
Flist
.
(I)
…
CALC
á
LnReg
â
12
.
16
log
value
Returns logarithm of
value
.
(F)
«
2
.
4
log
list
Returns logarithm of
list
elements.
(F)
«
2
.
4
max(
valueA
,
valueB
)
Returns larger of
valueA
and
valueB
.
(F)
NUM
á
max(
â
2
.
10
max(
list
)
Returns largest element in
list
.
(F)
y
ã
LIST
ä
MATH
á
max(
â
11
.
9
max(
listA
,
listB
)
Returns a list of the larger
of each pair of elements in
listA
and
listB
.
(F)
y
ã
LIST
ä
MATH
á
max(
â
11
.
9
mean(
list
)
Returns the mean of
list
.
(F)
y
ã
LIST
ä
MATH
á
mean(
â
11
.
9
mean(
list
,
Flist
)
Returns the mean of
list
with frequency
Flist
.
(F)
y
ã
LIST
ä
MATH
á
mean(
â
11
.
9
Med
.
Med
Fits data to median-
median model using lists
from
SET
UP
CALCS
.
(I)
…
CALC
á
Med-Med
â
12
.
15
Med
.
Med
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
median-median model.
(I)
…
CALC
á
Med-Med
â
12
.
15
Med
.
Med
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
median-median model
with frequency
Flist
.
(I)
…
CALC
á
Med-Med
â
12
.
15
median(
list
)
Returns the median of
list
.
(F)
y
ã
LIST
ä
MATH
á
median(
â
11
.
9
median(
list
,
Flist
)
Returns the median of
list
with frequency
Flist
.
(F)
y
ã
LIST
ä
MATH
á
median(
â
11
.
9
Menu("
title
","
text
",
label
,
"
text
",
label
,
. . .
)
Sets up branches for up to
7 menu items.
(I)
†
CTL
á
Menu(
â
13
.
11
min(
valueA
,
valueB
)
Returns smaller of
valueA
and
valueB
.
(F)
NUM
á
min(
â
2
.
10
min(
list
)
Returns smallest element
in
list
.
(F)
y
ã
LIST
ä
MATH
á
min(
â
11
.
9
min(
listA
,
listB
)
Returns list of smaller of
each pair of elements in
listA
and
listB
.
(F)
y
ã
LIST
ä
MATH
á
min(
â
11
.
9
A-12 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 12 of 28
Minute notation:
degrees
'
minutes
'
seconds
'
Interprets angle as
degrees
,
minutes
, and
seconds
.
(F)
y
ã
ANGLE
ä
á
'
â
2
.
13
Multiplication:
valueA
…
valueB
Returns
valueA
times
valueB
.
(F)
¯
2
.
3
Multiplication:
value
…
list
Returns
value
times each
list
element.
(F)
¯
2
.
3
Multiplication:
list
…
value
Returns each
list
element
times
value
.
(F)
¯
2
.
3
Multiplication:
listA
…
listB
Returns
listA
elements
times
listB
elements.
(F)
¯
2
.
3
Multiplication:
value
…
matrix
Returns
value
times
matrix
elements.
(F)
¯
10-10
Multiplication:
matrixA
…
matrixB
Returns
matrixA
times
matrixB
.
(F)
¯
10-10
items
nCr
number
Returns combinations of
items
(integer
‚
0) taken
number
(integer
‚
0) at a
time.
(F)
PRB
á
nCr
â
2
.
12
nDeriv(
expression
,
variable
,
value
)
Returns approximate
numerical derivative of
expression
with respect
to
variable
at
value
.
H
is
1
E
L
3.
(F)
MATH
á
nDeriv(
â
2
.
7
nDeriv(
expression
,
variable
,
value
,
H
)
Returns approximate
numerical derivative of
expression
with respect
to
variable
at
value
, with
specified
H
.
(F)
MATH
á
nDeriv(
â
2
.
7
Negation:
M
value
Returns negative of
value
.
(F)
Ì
2
.
4
Negation:
M
list
Returns
list
with each
element negated.
(F)
Ì
2
.
4
Negation:
M
matrix
Returns
matrix
with each
element negated.
(F)
Ì
10
.
10
Tables A-13
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 13 of 28
Normal
Sets normal display
MODE
.
(I)
†
z
á
Normal
â
1
.
10
not
value
Returns 0 if
value
is
ƒ
0.
(F)
y
ã
TEST
ä
LOGIC
á
not
â
2
.
16
Not equal:
valueA
ƒ
valueB
Returns 1 if
valueA ƒ
valueB
. Returns 0 if
valueA
=
valueB
.
(F)
y
ã
TEST
ä
TEST
á
ƒ
â
2
.
15
Not equal:
listA
ƒ
listB
Returns 1 if
listA
element
ƒ
listB
element.
Otherwise, returns 0.
(F)
y
ã
TEST
ä
TEST
á
ƒ
â
2
.
15
Not equal:
matrixA
ƒ
matrixB
Returns 1 if
matrixA
element
ƒ
matrixB
element. Otherwise,
returns 0.
(F)
y
ã
TEST
ä
TEST
á
ƒ
â
10
.
11
items
nPr
number
Returns permutations of
items
(0
integer) taken
number
(0
integer) at a
time.
(F)
PRB
á
nPr
â
2
.
12
1
.
Var
Stats
Performs one-variable
analysis using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
1-Var
Stats
â
12
.
14
1
.
Var
Stats
Xlist
Performs one-variable
analysis using
Xlist
and a
frequency of 1.
(I)
…
CALC
á
1-Var
Stats
â
12
.
14
1
.
Var
Stats
Xlist
,
Flist
Performs one-variable
analysis using
Xlist
and
frequencies from
Ylist
.
(I)
…
CALC
á
1-Var
Stats
â
12
.
14
valueA
or
valueB
Returns 1 if
valueA
or
valueB
is
ƒ
0.
(F)
y
ã
TEST
ä
LOGIC
á
or
â
2
.
16
Output(
line
,
column
,"
text
")
Displays
text
beginning at
specified
line
and
column
.
(I)
†
I/O
á
Output(
â
13
.
15
Output(
line
,
column
,
value
)
Displays
value
beginning
at specified
line
and
column
.
(I)
†
I/O
á
Output(
â
13
.
15
A-14 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 14 of 28
Par
Sets parametric graphing
MODE
.
(I)
†
z
á
Par
â
1
.
11
Pause
Suspends program
execution until
Í
is
pressed.
(I)
†
CTL
á
Pause
â
13
.
10
Pause
value
Displays
value
, suspends
program execution until
Í
is pressed.
(I)
†
CTL
á
Pause
â
13
.
10
Plot
#
(
type
,
Xlist
,
Ylist
,
mark
)
Defines
Plot
#
(1–3) of
type
Scatter
or
xyLine
for
X
list
and
Ylist
using
mark
.
(I)
†
y
ã
STAT PLOT
ä
á
Plot#
â
12
.
20
Plot
#
(
type
,
Xlist
,
Flist
)
Defines
Plot
#
(1–3) of
type
Histogram
or
Boxplot
for
Xlist
with
frequency
Flist
.
(I)
†
y
ã
STAT PLOT
ä
á
Plot#
â
12
.
20
PlotsOff
Deselects all stat plots.
(I)
†
y
ã
STAT PLOT
ä
á
PlotsOff
â
12
.
21
PlotsOff
plot#
,
plot#
,
. . . Deselects stat
Plot1
,
Plot2
, or
Plot3
.
(I)
†
y
ã
STAT PLOT
ä
á
PlotsOff
â
12
.
21
PlotsOn
Selects all stat plots.
(I)
†
y
ã
STAT PLOT
ä
á
PlotsOn
â
12
.
21
PlotsOn
plot#
,
plot#
,
. . . Selects stat
Plot1
,
Plot2
,
or
Plot3
.
(I)
†
y
ã
STAT PLOT
ä
á
PlotsOn
â
12
.
21
Pol
Sets polar graphing
MODE
.
(I)
†
z
á
Pol
â
1
.
11
PolarGC
Sets polar graphing
coordinates.
(I)
†
p
FORMAT
á
PolarGC
â
3
.
10
Power of ten:
10^
value
Returns 10 raised to
value
power.
(F)
y
ã
10
x
ä
2
.
4
Power of ten:
10^
list
Returns list of 10 raised
to
list
power.
(F)
y
ã
10
x
ä
2
.
4
Powers:
value
^
power
Returns
value
raised to
p
ower
.
(F)
›
2
.
3
Powers:
list
^
power
Returns
list
elements
raised to
power
.
(F)
›
2
.
3
Powers:
value
^
list
Returns
value
raised to
list
elements.
(F)
›
2
.
3
Powers:
matrix
^
power
Returns
matrix
elements
raised to
power
.
(F)
›
10
.
11
prgm
name
Executes program
name
.
(I)
CTRL
á
prgm
â
13
.
11
PrintScreen
Sends current display to
printer.
(I)
†
I/O
á
PrintScreen
â
13
.
17
Tables A-15
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 15 of 28
prod
list
Returns product of
list
elements.
(F)
y
ã
LIST
ä
MATH
á
prod
â
11
.
10
Prompt
varA
,
varB
,
. . . Prompts for value for
varA
, then
varB
, etc.
(I)
†
I/O
á
Prompt
â
13
.
15
P
8
Rx(
R
,
q
)
Returns
X
, given polar
coordinates
R
and
q
.
(F)
y
ã
ANGLE
ä
á
P
8
Rx(
â
2
.
14
P
8
Ry(
R
,
q
)
Returns
Y
, given polar
coordinates
R
and
q
.
(F)
y
ã
ANGLE
ä
á
P
8
Ry(
â
2
.
14
Pt
.
Change(
X
,
Y
)
Changes point at (
X
,
Y
).
(I)
y
ã
DRAW
ä
POINTS
á
Pt-Change(
â
8
.
12
Pt
.
Off(
X
,
Y
)
Erases point at (
X
,
Y
).
(I)
y
ã
DRAW
ä
POINTS
á
Pt-Off(
â
8
.
12
Pt
.
On(
X
,
Y
)
Draws point at (
X
,
Y
).
(I)
y
ã
DRAW
ä
POINTS
á
Pt-On(
â
8
.
12
PwrReg
Fits data to power model
using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
PwrReg
â
12
.
16
PwrReg
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
power model.
(I)
…
CALC
á
PwrReg
â
12
.
16
PwrReg
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
power model with
frequency
Flist
.
(I)
…
CALC
á
PwrReg
â
12
.
16
Pxl
.
Change(
row
,
column
)
Changes pixel at (
row
,
column
); 0
row
62 and
0
column
94.
(I)
y
ã
DRAW
ä
POINTS
á
Pxl-Change(
â
8
.
13
Pxl
.
Off(
row
,
column
)
Erases pixel at (
row
,
column
); 0
row
62 and
0
column
94.
(I)
y
ã
DRAW
ä
POINTS
á
Pxl-Off(
â
8
.
13
Pxl
.
On(
row
,
column
)
Draws pixel at (
row
,
column
); 0
row
62 and
0
column
94.
(I)
y
ã
DRAW
ä
POINTS
á
Pxl-On(
â
8
.
13
pxl
.
Test(
row
,
column
)
Returns 1 if pixel (
row
,
column
) is on, 0 if it is off;
0
row
62 and
0
column
94.
(F)
y
ã
DRAW
ä
POINTS
á
pxl-Test(
â
8
.
13
QuadReg
Fits data to quadratic
model using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
QuadReg
â
12
.
15
QuadReg
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
quadratic model.
(I)
…
CALC
á
QuadReg
â
12
.
15
QuadReg
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
quadratic model with
frequency
Flist
.
(I)
…
CALC
á
QuadReg
â
12
.
15
A-16 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 16 of 28
QuartReg
Fits data to quartic model
using lists from
SET
UP
CALCS
.
(I)
…
CALC
á
QuartReg
â
12
.
15
QuartReg
Xlist
,
Ylist
Fits
Xlist
and
Ylist
to
quartic model.
(I)
…
CALC
á
QuartReg
â
12
.
15
QuartReg
Xlist
,
Ylist
,
Flist
Fits
Xlist
and
Ylist
to
quartic model with
frequency
Flist
.
(I)
…
CALC
á
QuartReg
â
12
.
15
angle
r
Interprets
angle
as
radians.
(F)
y
ã
ANGLE
ä
á
r
â
2
.
13
Radian
Sets radian
MODE
.
(I)
†
z
á
Radian
â
1
.
11
rand
Returns random number
between 0 and 1.
(F)
PRB
á
rand
â
2
.
12
randM(
rows
,
columns
)
Returns a
rows
(1–99) ×
columns
(1–99) random
matrix.
(F)
MATH
á
randM(
â
10
.
13
RecallGDB
GDB
n
Recalls graph database
GDB
n
as the current
graph.
(I)
y
ã
DRAW
ä
STO
á
RecallGDB
â
8
.
15
RecallPic
Pic
n
Recalls picture
Pic
n
onto
current graph.
(I)
y
ã
DRAW
ä
STO
á
RecallPic
â
8
.
14
RectGC
Sets rectangular graphing
coordinates.
(I)
†
p
FORMAT
á
RectGC
â
3
.
10
Repeat
condition
:
commands
:End
Execute
commands
until
condition
is true.
(I)
†
CTL
á
Repeat
â
13
.
9
Return
Returns to calling
program.
(I)
†
CTL
á
Return
â
13
.
12
n
th
root
x
‡
value
Returns
n
th
root
of
value
.
(F)
MATH
á
x
‡
â
2
.
6
n
th
root
x
‡
list
Returns
n
th
root
of
list
elements.
(F)
MATH
á
x
‡
â
2
.
6
list
x
‡
value
Returns
list
roots of
value
.
(F)
MATH
á
x
‡
â
2
.
6
listA
x
‡
listB
Returns
list
roots of
list
.
(F)
MATH
á
x
‡
â
2
.
6
round(
value
)
Returns
value
rounded to
10 digits.
(F)
NUM
á
round(
â
2
.
9
round(
value
,
#decimals
)
Returns
value
rounded to
#
decimals
(
9).
(F)
NUM
á
round(
â
2
.
9
round(
list
)
Returns
list
elements
rounded to 10 digits.
(F)
NUM
á
round(
â
2
.
9
Tables A-17
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 17 of 28
round(
list
,
#decimals
)
Returns
list
elements
rounded to #
decimals
(
9).
(F)
NUM
á
round(
â
2
.
9
round(
matrix
)
Returns
matrix
elements
rounded to 10 digits.
(F)
NUM
á
round(
â
10
.
11
round(
matrix
,
#decimals
)
Returns
matrix
elements
rounded to #
decimals
.
(F)
NUM
á
round(
â
10
.
11
rowSwap(
matrix
,
rowA
,
rowB
)
Returns matrix with
rowA
of
matrix
swapped with
rowB
.
(F)
MATH
á
rowSwap(
â
10
.
14
row+(
matrix
,
rowA
,
rowB
)
Returns matrix with
rowA
of
matrix
added to
rowB
and stored in
rowB
.
(F)
MATH
á
row+(
â
10
.
14
…
row(
value
,
matrix
,
row
)
Returns matrix with
row
of
matrix
multiplied by
value
and stored in
row
.
(F)
MATH
á
…
row(
â
10
.
14
…
row+(
value
,
matrix
,
rowA
,
rowB
)
Returns matrix with
rowA
of
matrix
multiplied by
value
, added to
rowB
, and
stored in
rowB
.
(F)
MATH
á
…
row+(
â
10
.
14
R
8
Pr(
X
,
Y
)
Returns
R
, given
rectangular coordinates
X
and
Y
.
(F)
y
ã
ANGLE
ä
á
R
8
Pr(
â
2
.
14
R
8
P
q
(
X
,
Y
)
Returns
q
, given
rectangular coordinates
X
and
Y
.
(F)
y
ã
ANGLE
ä
á
R
8
P
q
(
â
2
.
14
Sci
Sets scientific display
MODE
.
(I)
z
á
Sci
â
1
.
10
Send(
variable
)
Sends contents of
variable
to external
device.
(I)
†
I/O
á
Send(
â
13
.
17
Seq
Sets
MODE
to graph
sequences.
(I)
†
z
á
Seq
â
1
.
11
seq(
expression
,
variable
,
begin
,
end
,
increment
)
Returns list created by
evaluating
expression
for
variable
, from
begin
to
end
at
increment.
(F)
y
ã
LIST
ä
OPS
á
seq(
â
11
.
8
Sequential
Sets
MODE
to graph
sequentially.
(I)
†
z
á
Sequential
â
1
.
11
A-18 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 18 of 28
Shade(
lowerfunc
,
upperfunc
)
Shade area above
lowerfunc
and below
upperfunc
.
(I)
y
ã
DRAW
ä
DRAW
á
Shade(
â
8
.
8
Shade(
lowerfunc
,
upperfunc
,
resolution
)
Shade area above
lowerfunc
, below
upperfunc
with
1<
resolution
<9.
(I)
y
ã
DRAW
ä
DRAW
á
Shade(
â
8
.
8
Shade(
lowerfunc
,
upperfunc
,
resolution
,
Xleft
)
Shade area above
lowerfunc
, below
upperfunc
, to right of
X
=
Xleft
, with
1<
resolution
<9.
(I)
y
ã
DRAW
ä
DRAW
á
Shade(
â
8
.
8
Shade(
lowerfunc
,
upperfunc
,
resolution
,
Xleft
,
Xright
)
Shade area above
lowerfunc
, below
upperfunc
, to right of
X
=
Xleft
, to left of
X
=
Xright
, with
1<
resolution
<9.
(I)
y
ã
DRAW
ä
DRAW
á
Shade(
â
8
.
8
Simul
Sets simultaneous
graphing
MODE
.
(I)
†
z
á
Simul
â
1
.
11
sin
value
Returns sine of
value
.
(F)
˜
2
.
3
sin
list
Returns sine of
list
elements.
(F)
˜
2
.
3
sin
M
1
value
Returns arcsine of
value
.
(F)
y
ã
sin
M
1
ä
2
.
3
sin
M
1
list
Returns arcsine of
list
elements.
(F)
y
ã
sin
M
1
ä
2
.
3
sinh
value
Returns hyperbolic sine of
value
.
(F)
HYP
á
sinh
â
2
.
11
sinh
list
Returns hyperbolic sine of
list
elements.
(F)
HYP
á
sinh
â
2
.
11
sinh
M
1
value
Returns hyperbolic
arcsine of
value
.
(F)
HYP
á
sinh
M
1
â
2
.
11
sinh
M
1
list
Returns hyperbolic
arcsine of
list
elements.
(F)
HYP
á
sinh
M
1
â
2
.
11
solve(
expression
,
variable
,
guess
)
Solves
expression
for
variable
using
guess
(a
number or 2-element list),
within bounds
L
1
E
99 and
1
E
99.
(F)
MATH
á
solve(
â
2
.
8
Tables A-19
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 19 of 28
solve(
expression
,
variable
,
guess
,{
lower
,
upper
})
Solves
expression
for
variable
using
guess
(a
number or 2-element list),
between
lower
and
upper
.
(F)
MATH
á
solve(
â
2
.
8
SortA(
listname
)
Sorts
listname
elements
in ascending order.
(I)
y
ã
LIST
ä
OPS
á
SortA(
â
11
.
6
SortA(
listnameI
,
listnameD
,
listnameD
,
...
)
Sorts elements of
listnameI
in ascending
order and
listnameD
as
dependent lists.
(I)
y
ã
LIST
ä
OPS
á
SortA(
â
11
.
6
SortD(
listname
)
Sorts elements of
listname
in descending
order.
(I)
y
ã
LIST
ä
OPS
á
SortD(
â
11
.
6
SortD(
listnameI
,
listnameD
,
listnameD
,
...
)
Sorts elements of
listnameI
in descending
order and
listnameD
as
dependent lists.
(I)
y
ã
LIST
ä
OPS
á
SortD(
â
11
.
6
Split
Sets split screen display
MODE
.
(I)
†
z
á
Split
â
1
.
11
Square root:
‡
value
Returns square root of
value
.
(F)
y
ã
‡
ä
2
.
3
Square root:
‡
list
Returns square root of
list
elements.
(F)
y
ã
‡
ä
2
.
3
Squaring:
value
2
Returns
value
multiplied
by itself.
(F)
¡
2
.
3
Squaring:
list
2
Returns
list
elements
squared.
(F)
¡
2
.
3
Squaring:
matrix
2
Returns
matrix
multiplied
by itself.
(F)
¡
10
.
11
Stop
Ends program execution,
returns to Home screen.
(I)
†
CTL
á
Stop
â
13
.
12
Store:
value
!
variable
Stores
value
to
variable
.
(I)
¿
1
.
13
StoreGDB
GDB
n
Stores current graph as
database
GDB
n
.
(I)
y
ã
DRAW
ä
STO
á
StoreGDB
â
8
.
15
StorePic
Pic
n
Stores current picture as
picture
Pic
n
.
(I)
y
ã
DRAW
ä
STO
á
StorePic
â
8
.
14
Subtraction:
valueA
–v
alueB
Subtracts
valueB
from
valueA
.
(F)
¹
2
.
3
Subtraction:
value
–
list
Subtracts
list
elements
from
value
.
(F)
¹
2
.
3
Subtraction:
list
–v
alue
Subtracts
value
from
list
elements.
(F)
¹
2
.
3
A-20 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 20 of 28
Subtraction:
listA
–
listB
Subtracts
listB
elements
from
listA
elements.
(F)
¹
2
.
3
Subtraction:
matrixA
–
matrixB
Subtracts
matrixB
elements from
matrixA
elements.
(F)
¹
10
.
10
sum
list
Returns sum of elements
of
list
.
(F)
y
ã
LIST
ä
MATH
á
sum
â
11
.
10
tan
value
Returns tangent of
value
.
(F)
š
2
.
3
tan
list
Returns tangent of
list
elements.
(F)
š
2
.
3
tan
M
1
value
Returns arctangent of
value
.
(F)
y
ã
tan
M
1
ä
2
.
3
tan
M
1
list
Returns arctangent of
list
elements.
(F)
y
ã
tan
M
1
ä
2
.
3
Tangent(
expression
,
value
)
Draws line tangent to
expression
at
X
=
value
.
(I)
y
ã
DRAW
ä
DRAW
á
Tangent(
â
8
.
6
tanh
value
Returns hyperbolic
tangent of
value
.
(F)
HYP
á
tanh
â
2
.
11
tanh
list
Returns hyperbolic
tangent of
list
elements.
(F)
HYP
á
tanh
â
2
.
11
tanh
M
1
value
Returns hyperbolic
arctangent of
value
.
(F)
HYP
á
tanh
M
1
â
2
.
11
tanh
M
1
list
Returns hyperbolic
arctangent of
list
elements.
(F)
HYP
á
tanh
M
1
â
2
.
11
Text(
row
,
column
,
valueA
,
valueB
. . .
)
Writes value of
valueA
(which can be
"
text
"
) on
graph beginning at pixel
(
row
,
column
). 0
row
57,
0
column
94.
(I)
y
ã
DRAW
ä
DRAW
á
Text(
â
8
.
10
Then
See
If:Then
Time
Sets sequence graphs to
plot over time.
(I)
†
p
FORMAT
á
Time
â
6
.
5
Trace
Displays graph and enters
TRACE
mode.
(I)
†
r
3
.
14
Transpose:
matrix
T
Returns
matrix
with
elements transposed.
(F)
MATH
á
T
â
10
.
12
Tables A-21
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 21 of 28
2-Var
Stats
Performs two-variable
analysis using lists from
SET
UP
CALCS
menu.
(I)
…
CALC
á
2-Var Stats
â
12
.
14
2-Var
Stats
Xlist
,
Ylist
Performs two-variable
analysis using
Xlist
and
Ylist
.
(I)
…
CALC
á
2-Var Stats
â
12
.
14
2-Var
Stats
Xlist
,
Ylist
,
Flist
Performs two-variable
analysis using
Xlist
and
Ylist
with frequency
Flist
.
(I)
…
CALC
á
2-Var Stats
â
12
.
14
Vertical
X
Draws vertical line at
X
.
(I)
y
ã
DRAW
ä
DRAW
á
Vertical
â
8
.
5
Web
Sets sequence graphs to to
trace as webs.
(I)
†
p
FORMAT
á
Web
â
6
.
5
While
condition
:
commands
:End
Executes
commands
while
condition
is true.
(I)
†
CTL
á
While
â
13
.
9
valueA
xor
valueB
Returns 1 if only
valueA
or
valueB
= 0.
(F)
y
ã
TEST
ä
LOGIC
á
xor
â
2
.
16
ZBox
Displays graph to allow
user to define new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZBox
â
3
.
16
ZDecimal
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZDecimal
â
3
.
18
ZInteger
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZInteger
â
3
.
18
Zoom In
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
Zoom In
â
3
.
17
Zoom Out
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
Zoom Out
â
3
.
17
ZoomRcl
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZoomRcl
â
3
.
19
ZoomSto
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZoomSto
â
3
.
19
ZoomStat
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZoomStat
â
3
.
18
ZPrevious
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZPrevious
â
3
.
19
ZSquare
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZSquare
â
3
.
18
ZStandard
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZStandard
â
3
.
18
ZTrig
Displays graph in new
v
iewing
WINDOW
.
(I)
q
ZOOM
á
ZTrig
â
3
.
18
A-22 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 22 of 28
TI-82 Menu Map
Menus begin in the upper left of the keyboard. Default values are shown.
o
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func MODE)
Y
1
=
Y
2
=
Y
3
=
Y
4
=
...
Y
9
=
Y
0
=
(Par MODE)
X
1T
=
Y
1T
=
X
2T
=
Y
2T
=
...
X
6T
=
Y
6T
=
(Pol MODE)
r
1
=
r
2
=
r
3
=
r
4
=
r
5
=
r
6
=
(Seq MODE)
Un=
Vn=
p
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func MODE)
WINDOW
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
(Par MODE)
WINDOW
Tmin=0
Tmax=
p…
2
Tstep=
pà
24
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
(Pol MODE)
WINDOW
q
min=0
q
max=
p…
2
q
step=
pà
24
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
(Seq MODE)
WINDOW
UnStart=0
VnStart=0
nStart=0
nMin=0
nMax=10
Xmin=-10
Xmax=10
Xscl=1
Ymin=-10
Ymax=10
Yscl=1
p
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func/Par/Pol MODE)
FORMAT
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
(Seq MODE)
FORMAT
Time Web
RectGC PolarGC
CoordOn CoordOff
GridOff GridOn
AxesOn AxesOff
LabelOff LabelOn
q
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
q
À
ÄÄÄÄÄÄÄÄ¿
ZOOM
1:ZBox
2:Zoom In
3:Zoom Out
4:ZDecimal
5:ZSquare
6:ZStandard
7:ZTrig
8:ZInteger
9:ZoomStat
MEMORY
1:ZPrevious
2:ZoomSto
3:ZoomRcl
4:SetFactors…
ZOOM FACTORS
XFact=4
YFact=4
Tables A-23
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 23 of 28
y
ã
CALC
ä
ÚÄÄÄ
Á
ÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Func MODE)
CALCULATE
1:value
2:root
3:minimum
4:maximum
5:intersect
6:dy/dx
7:
‰
f(x)dx
(Par MODE)
CALCULATE
1:value
2:dy/dx
3:dy/dt
4:dx/dt
(Pol MODE)
CALCULATE
1:value
2:dy/dx
3:dr/d
q
(Seq MODE)
(Time FORMAT)
CALCULATE
1:value
y
ã
TblSet
ä
ÚÄÄÄ
Ù
y
ã
TblSet
ä
ÚÄÄÄÄ
Ù
z
Ú
Ù
TABLE SETUP
TblMin=0
@
Tbl=1
Indpnt: Auto Ask
Depend: Auto Ask
(PRGM editor)
TABLE SETUP
Indpnt: Auto Ask
Depend: Auto Ask
Normal Sci Eng
Float 0123456789
Radian Degree
Func Par Pol Seq
Connected Dot
Sequential Simul
FullScreen Split
y
ã
STAT PLOT
ä
ÚÄÄÄÄÄ
Ù
y
ã
STAT PLOT
ä
ÚÄÄÄÄÄ
Á
ÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
STAT PLOTS
1:Plot1…
Off
"
L
1
L
2
›
2:Plot2…
Off
"
L
1
L
2
›
3:Plot3…
Off
"
L
1
L
2
›
4:PlotsOff
5:PlotsOn
(PRGM editor)
PLOTS
1:Plot1(
2:Plot2(
3:Plot3(
4:PlotsOff
5:PlotsOn
(PRGM editor)
TYPE
1:Scatter
2:xyLine
3:Boxplot
4:Histogram
(PRGM editor)
MARK
1:
›
2:+
3:
¦
…
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄ¿
…
Ú
Ù
EDIT
1:Edit…
2:SortA(
3:SortD(
4:ClrList
CALC
1:1-Var Stats
2:2-Var Stats
3:SetUp…
4:Med-Med
5:LinReg(ax+b)
6:QuadReg
7:CubicReg
8:QuartReg
9:LinReg(a+bx)
0:LnReg
A:ExpReg
B:PwrReg
(SetUp…)
1-Var Stats
Xlist:
L1
L2
L3
L4
L5
L6
Freq:
1 L1
L2
L3
L4
L5
L6
2-Var Stats
Xlist:
L1
L2
L3
L4
L5
L6
Ylist:
L1
L2
L3
L4
L5
L6
Freq:
1 L1
L2
L3
L4
L5
L6
A-24 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 24 of 28
y
ã
LIST
ä
ÚÄÄ
Á
ÄÄÄÄÄÄÄÄÄÄ¿
OPS
1:SortA(
2:SortD(
3:dim
4:Fill(
5:seq(
MATH
1:min(
2:max(
3:mean(
4:median(
5:sum
6:prod
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
MATH
1:
8
Frac
2:
8
Dec
3:
3
4:
3
‡
5:
x
‡
6:fMin(
7:fMax(
8:nDeriv(
9:fnInt(
0:solve(
NUM
1:round(
2:iPart
3:fPart
4:int
5:min(
6:max(
HYP
1:sinh
2:cosh
3:tanh
4:sinh
-
1
5:cosh
-
1
6:tanh
-
1
PRB
1:rand
2:nPr
3:nCr
4:!
y
ã
TEST
ä
ÚÄÄÄÄ
Á
ÄÄÄÄÄÄÄÄ¿
TEST
1:=
2:
ƒ
3:>
4:
‚
5:<
6:
LOGIC
1:and
2:or
3:xor
4:not
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
y
ã
ANGLE
ä
ÚÄÄÄÄ
Ù
NAMES
1:[A]
row
x
col
2:[B]
row
x
col
3:[C]
row
x
col
4:[D]
row
x
col
5:[E]
row
x
col
MATH
1:det
2:
T
3:dim
4:Fill(
5:identity
6:randM(
7:augment(
8:rowSwap(
9:row+(
0:
…
row(
A:
…
row+(
EDIT
1:[A]
row
x
col
2:[B]
row
x
col
3:[C]
row
x
col
4:[D]
row
x
col
5:[E]
row
x
col
ANGLE
1:
¡
2:'
3:
r
4:
8
DMS
5:R
8
Pr(
6:R
8
P
q
(
7:P
8
Rx(
8:P
8
Ry(
Tables A-25
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 25 of 28
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
EXEC
1:
name
2:
name
3:
name
...
EDIT
1:
name
2:
name
3:
name
...
New
1:Create New
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(PRGM editor)
CTL
1:If
2:Then
3:Else
4:For(
5:While
6:Repeat
7:End
8:Pause
9:Lbl
0:Goto
A:IS>(
B:DS<(
C:Menu(
D:prgm
E:Return
F:Stop
(PRGM editor)
I/O
1:Input
2:Prompt
3:Disp
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHome
9:ClrTable
0:PrintScreen
A:Get(
B:Send(
(PRGM editor)
EXEC
1:
name
2:
name
3:
name
...
y
ã
DRAW
ä
ÚÄÄÄÄÄ
Á
ÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
DRAW
1:ClrDraw
2:Line(
3:Horizontal
4:Vertical
5:Tangent(
6:DrawF
7:Shade(
8:DrawInv
9:Circle(
0:Text(
A:Pen
POINTS
1:Pt-On(
2:Pt-Off(
3:Pt-Change(
4:Pxl-On(
5:Pxl-Off(
6:Pxl-Change(
7:pxl-Test(
STO
1:StorePic
2:RecallPic
3:StoreGDB
4:RecallGDB
A-26 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 26 of 28
Ú
Ù
VARS
1:Window…
2:Zoom…
3:GDB…
4:Picture…
5:Statistics…
6:Table…
Ú
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄ
(Window…)
X/Y
1:Xmin
2:Xmax
3:Xscl
4:Ymin
5:Ymax
6:Yscl
7:
@
X
8:
@
Y
9:XFact
0:YFact
(Window…)
T/
q
1:Tmin
2:Tmax
3:Tscl
4:
q
min
5:
q
max
6:
q
step
(Window…)
U/V
1:UnStart
2:VnStart
3:nStart
4:nMin
5:nMax
(Zoom…)
ZX/ZY
1:ZXmin
2:ZXmax
3:ZXscl
4:ZYmin
5:ZYmax
6:ZYscl
(Zoom…)
ZT/Z
q
1:ZTmin
2:ZTmax
3:ZTscl
4:Z
q
min
5:Z
q
max
6:Z
q
step
ÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄ
(Zoom…)
ZU
1:ZUnStart
2:ZVnStart
3:ZnStart
4:ZnMin
5:ZnMax
(GDB…)
GDB
1:GDB1
2:GDB2
3:GDB3
4:GDB4
5:GDB5
6:GDB6
(Picture…)
PIC
1:Pic1
2:Pic2
3:Pic3
4:Pic4
5:Pic5
6:Pic6
(Statistics…)
X/Y
1:n
2:
v
3:Sx
4:
s
x
5:
w
6:Sy
7:
s
y
8:minX
9:maxX
0:minY
A:maxY
(Statistics…)
G
1:
G
x
2:
G
x
2
3:
G
y
4:
G
y
2
5:
G
xy
ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Statistics…)
EQ
1:a
2:b
3:c
4:d
5:e
6:r
7:RegEQ
(Statistics…)
BOX
1:Q
1
2:Med
3:Q
3
(Statistics…)
PTS
1:x
1
2:y
1
3:x
2
4:y
2
5:x
3
6:y
3
(Table…)
TABLE
1:TblMin
2:
@
Tbl
3:TblInput
Tables A-27
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 27 of 28
y
ã
Y-VARS
ä
ÚÄÄ
Ù
Y-Vars
1:Function…
2:Parametric…
3:Polar…
4:Sequence…
5:On/Off…
y
ã
Y-VARS
ä
ÚÄÄÄÄ
Á
ÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿
(Function…)
FUNCTION
1:Y
1
2:Y
2
3:Y
3
4:Y
4
...
9:Y
9
0:Y
0
(Parametric…)
PARAMETRIC
1:X
1
T
2:Y
1
T
3:X
2
T
4:Y
2
T
...
A:X
6T
B:Y
6T
(Polar…)
1:r
1
=
2:r
2
=
3:r
3
=
4:r
4
=
5:r
5
=
6:r
6
=
(Sequence…)
SEQUENCE
1:Un
2:Vn
(On/Off…)
ON/OFF
1:FnOn
2:FnOff
y
ã
MEM
ä
ÚÄÄ
Ù
y
ã
MEM
ä
ÚÄÄÄ
Á
ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
MEMORY
1:Check RAM…
2:Delete…
3:Reset…
(Check RAM…)
MEM FREE 28754
Real 15
List 0
Matrix 0
Y-Vars 240
Prgm 14
Pic 0
GDB 0
(Delete…)
DELETE FROM…
1:All…
2:Real…
3:List…
4:Matrix…
5:Y-Vars…
6:Prgm…
7:Pic…
8:GDB…
(Reset…)
RESET MEMORY
1:No
2:Reset
A-28 Tables
8299APPA.DOC TI-82, Appendix A, English Bob Fedorisko Revised: 02/09/01 9:35 AM Printed:
02/09/01 12:43 PM Page 28 of 28
Table of Variables
The variables listed below are used by the TI
.
82 in various ways. Some have
restrictions on their use.
User Variables
The variables
A
through
Z
and
q
are defined as real numbers. You may store
to them. However, the TI
.
82 can update
X
,
Y
,
R
,
q
, and
T
during graphing,
so you may wish to avoid using these variables for nongraphing activities.
The variables
L
1
through
L
6
are defined as lists. You cannot store another
type of data to them.
The variables
ã
A
ä
,
ã
B
ä
,
ã
C
ä
,
ã
D
ä
, and,
ã
E
ä
are defined as matrices. You cannot
store another type of data to them.
The variables
Pic1
through
Pic6
are pictures. You cannot store another type
of data to them.
The variables
GDB1
through
GDB6
are graph databases. You cannot store
another type of data to them.
You can store any string of characters, functions, instructions, or variable
names to the functions
Y
n
,
X
n
T
,
r
n
,
U
n
, and
V
n
directly or through the
Y=
editor. The validity of the string is determined when the function is
evaluated.
System Variables
The variables below must be real numbers. You may store to them. The
TI
.
82 can update some of them, as the result of a
ZOOM
, for example, so
you may wish to avoid using these variables for nongraphing activities.
¦
Xmin
,
Xmax
,
Xscl
,
@
X
,
XFact
,
Tstep
,
UStart
,
n
Min
, and other
WINDOW
variables.
¦
ZXmin
,
ZXmax
,
ZXscl
,
ZTstep
,
ZU
n
Start
,
Z
n
Min
, and other
ZOOM
MEMORY
variables.
The variables below are reserved for use by the TI
.
82. You cannot store to
them.
¦
n
,
v
,
minX
,
G
x
,
a
,
r
,
RegEQ
,
x
1
,
y
1
, and other statistical result variables.
¦
Q
1
,
Med
,
Q
3
.
You can store to
U
n
-
1
and
V
n
-
1
outside of graphing, but you cannot store to
n
outside of graphing.
Reference Information B-1
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 1 of 12
Appendix B: Reference Information
This appendix provides supplemental information that may be helpful as you use
the TI
.
82. It includes procedures that may help you correct problems with the
calculator.
Appendix Contetns
Battery Information
............................
B-2
In Case of Difficulty
............................
B-4
Accuracy Information
..........................
B-5
Error Conditions
..............................
B-7
Support and Service Information
...................
B-11
Warranty Information
...........................
B-12
B-2 Reference Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 2 of 12
Battery Information
The TI
.
82 uses two types of batteries: four AAA alkaline batteries and a lithium
battery as a backup for retaining memory while you change the AAA batteries.
When to Replace the Batteries
As the batteries run down, the display begins to dim (especially during
calculations), and you must adjust the contrast to a higher setting. If you
find it necessary to set the contrast to a setting of 8 or 9, you will need to
replace the batteries soon. You should change the lithium battery every
three or four years.
Effects of Replacing the Batteries
If you do not remove both types of batteries at the same time or allow them
to run down completely, you can change either type of battery without
losing anything in memory.
Battery Precautions
Take these precautions when replacing batteries.
¦
Do not mix new and used batteries. Do not mix brands (or types within
brands) of batteries.
¦
Do not mix rechargeable and nonrechargeable batteries.
¦
Install batteries according to polarity (+ and
N
) diagrams.
¦
Do not place nonrechargeable batteries in a battery recharger.
¦
Properly dispose of used batteries immediately. Do not leave them
within the reach of children.
¦
Do not incinerate batteries.
Reference Information B-3
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 3 of 12
Replacing the Batteries
1. Turn off the calculator. Replace the slide cover over the keyboard to
avoid inadvertently turning on the calculator. Turn the back of the
calculator toward you.
2. Hold the calculator upright. Place your thumb on the oval indentation
on the battery cover. Push down and toward you to slide the cover
about ¼ inch (6 mm). Lift off the cover to expose the battery
compartment.
Note: To avoid loss of information stored in memory, you must
turn off the calculator. Do not remove the AAA batteries and
the lithium battery simultaneously.
3. Replace all four AAA alkaline batteries at the same time. Or, replace the
lithium battery.
¦
To replace the AAA alkaline batteries, remove all four discharged
AAA batteries and install new ones according to the polarity
(+ and
N
) diagrams in the battery compartment.
¦
To remove the lithium battery, place your index finger on the
battery. Insert the tip of a ball-point pen (or similar instrument)
under the battery at the small opening provided in the battery
compartment. Carefully pry the battery upward, holding it with your
thumb and finger. (There is a spring that pushes against the
underside of the battery.)
¦
Install the new battery, + side up, by inserting the battery and gently
snapping it in with your finger. Use a CR1616 or CR1620 (or
equivalent) lithium battery.
4. Replace the battery compartment cover. Turn the calculator on and
adjust the display contrast, if necessary (step 1; page B
.
4).
B-4 Reference Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 4 of 12
In Case of Difficulty
If you have difficulty operating the calculator, the following suggestions may help
you to correct the problem.
Handling a Difficulty
1. If an error occurs, follow the procedure on page 1
.
22. Refer to the more
detailed explanations about specific errors beginning on page B
.
6, if
necessary.
2. If you cannot see anything on the display, follow the instructions on
page 1
.
3 to adjust the contrast.
3. If the cursor is a checker-board pattern, memory is full. Press
y
ã
MEM
ä
Delete...
and delete some items from memory.
4. If the dotted bar busy indicator is displayed, a graph or program is
paused and the TI
.
82 is waiting for input.
5. If the calculator does not appear to be working at all, be sure the
batteries are installed properly and that they are fresh.
Reference Information B-5
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 5 of 12
Accuracy Information
To maximize accuracy, the TI
.
82 carries more digits internally than it displays.
Computational Accuracy
Values in memory are stored using up to 14 digits with a 2-digit exponent.
¦
You can store a value in the
WINDOW
variables using up to 10 digits (12
digits for
Xscl
,
Yscl
,
Tstep
, and
q
step
).
¦
When a value is displayed, the displayed value is rounded as specified
by the
MODE
setting (Chapter 1), with a maximum of 10 digits and a 2-
digit exponent.
¦
RegEQ
displays up to 14 digits.
Graphing Accuracy
Xmin
is the center of the leftmost pixel,
Xmax
is the center of the next to
the right-most pixel. (The right-most pixel is reserved for the busy
indicator.)
@
X
is the distance between the centers of two adjacent pixels.
¦
@
X
is calculated as (
Xmax
N
Xmin
)
à
94
.
¦
If
@
X
is entered from the Home screen or a program, then
Xmax
is
calculated as
Xmin+
@
X
…
94
.
Ymin
is the center of the next to the bottom pixel,
Ymax
is the center of the
top pixel.
@
Y
is the distance between the centers of two adjacent pixels.
¦
@
Y
is calculated as (
Ymax
N
Ymin
)
à
62
.
¦
If
@
Y
is entered from the Home screen or a program, then
Ymax
is
calculated as
Ymin+
@
Y
…
62
.
Cursor coordinates are displayed as eight characters (which may include a
negative sign, decimal point, and exponent). The values of
X
and
Y
are
updated with a maximum of eight-digit accuracy.
minimum
,
maximum
, and
intersect
on the
CALCULATE
menu are
calculated with a tolerance of 1
E
L
5;
dy/dx
and
‰
f(x)dx
use a tolerance of
1
E
L
3. Therefore, the result displayed may not be accurate to all eight
displayed digits. (In general, for most functions, there are at least
5 accurate digits.) The tolerance can be specified for the command-line
functions
fMin(
,
fMax(
, and
fnInt(
on the
MATH MATH
menu.
B-6 Reference Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 6 of 12
Function Limits
Function Range of Input Values
sin
x
,
cos
x
,
tan
x
0
|
x
| < 10
12
(radian or degree)
arcsin
x
,
arccos
x L
1
x
1
ln
x
,
log
x
10
L
100
<
x
< 10
100
e
x
L
10
100
<
x
230.25850929940
10
x
L
10
100
<
x
< 100
sinh
x
,
cosh
x
|
x
|
230.25850929940
tanh
x
|
x
| < 10
100
sinh
-1
x
|
x
| < 5 × 10
99
cosh
-1
x
1
x
< 5 × 10
99
tanh
-1
x L
1 <
x
< 1
‡
x
0
x
< 10
100
x
!
0
x
69, where
x
is an integer
Function Results
Function Range of Result
sin
-1
x
,
tan
-1
x L
90
¡
to 90
¡
or
Lpà
2 to
pà
2 (radians)
cos
-1
x
0
¡
to 180
¡
or 0 to
p
(radians)
Reference Information B-7
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 7 of 12
Error Conditions
When the TI
.
82 detects an error, it displays ERR:
message
and the error menu.
The general procedure for correcting errors is described on page 1
.
22. Each error
type, including possible causes and suggestions for correction, are shown
below.
ARGUMENT
A function or instruction does not have the correct number of
arguments. See Appendix A and the appropriate chapter.
BAD GUESS
¦
For a
CALC
operation,
Guess
must be between
Lower Bound
and
Upper Bound
.
¦
For the
solve(
function,
guess
must be between
lower
and
upper
.
¦
The guess and several points around it are undefined.
Examine a graph of the function. If the equation has a solution,
change the bounds and/or the initial guess.
BOUND
¦
For a
CALC
operation , you must define
Lower Bound
<
Upper Bound
.
¦
For
fMin(
,
fMax(
,
fnInt(
, and
solve(
,
lower
must be less than
upper
.
BREAK
You have pressed the
É
key to break execution of a program,
halt a
DRAW
instruction, or stop evaluaton of an expression.
DATA TYPE
You have entered a value or variable that is the wrong data
type.
¦
A function (including implied multiplication) or an
instruction has an argument that is an invalid data type; for
example, a list where a real number is required. See
Appendix A and the appropriate chapter.
¦
In an editor, you have entered a type that is not allowed; for
example, a matrix as an element in the
STAT
list editor. See
the appropriate chapter.
¦
You are attempting to store to an incorrect data type; for
example, a matrix to a list.
DIM MISMATCH
You are attempting to perform an operation that has more than
one list or matrix, but the dimensions do not match.
B-8 Reference Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 8 of 12
DIVIDE BY 0
¦
You are attempting to divide by zero. This error does not
occur during graphing. The TI
.
82 allows for undefined
values on a graph.
¦
You are attempting a linear regression with a vertical line.
DOMAIN
¦
The argument to a function or instruction is out of the
valid range. See Appendix A and the appropriate chapter.
This error does not occur during graphing. The TI
.
82
allows for undefined values on a graph.
¦
You are attempting a logarithmic or power regression with
a
M
X
or an exponential regression with a
M
Y
.
Duplicate Name
Unable to transmit item because a variable with that name
already exists in receiving unit.
Error in Xmit
¦
Unable to transmit item. Check to see that the cable is
firmly connected to both units and that the receiving unit
is in
Receive
mode.
¦ É
was used to break during transmission.
ILLEGAL NEST
You are attempting to use an invalid function in an argument
to a function; for example,
seq(
within
expression
for
seq(
.
INCREMENT
¦
The increment in
seq(
is
0
or has the wrong sign. This
error does not occur during graphing. The TI
.
82 allows for
undefined values on a graph.
¦
The increment for a loop is
0
.
INVALID
You are attempting to reference a variable or use a function
in a place where it is not valid. For example,
Y
n
cannot
reference
Y
,
Xmin
,
@
X
or
TblMin
.
INVALID DIM
¦
The dimension of the argument is not appropriate for the
operation.
¦
Matrix element dimensions and list element dimensions
must be integers between 1 and 99.
¦
A matrix must be square to invert it.
ITERATIONS
solve(
has exceeded the maximum number of iterations
permitted. Examine a graph of the function. If the equation
has a solution, change the bounds and/or the initial guess.
Reference Information B-9
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 9 of 12
LABEL
The label in the
Goto
instruction is not defined with a
Lbl
instruction in the program.
MEMORY
There is insufficient memory in which to perform the desired
command. You must delete item(s) from memory (Chapter
15) before executing this command.
Recursive problems, such as
A=A+2:A
, display this error.
Interrupting an
If
/
Then
,
For
,
While
, or
Repeat
loop with a
Goto
that branches out of the loop can also cause this error,
because the
End
statement that terminates the loop is never
reached.
Memory Full
Unable to transmit item because there is insufficient
available memory in the receiving unit. You may skip the item
or exit
Receive
mode.
During a memory backup, the receiving unit does not have
enough memory to receive all items in memory in the sending
unit. A message indicates the number of bytes the sending
unit must delete to do the memory backup. Delete items and
try again.
MODE
You are attempting to store to a
WINDOW
variable in another
graphing
MODE
or to perform an instruction while in the
wrong
MODE
, such as
DrawInv
in a graphing
MODE
other
than
Func
.
OVERFLOW
You are attempting to enter, or have calculated, a number
that is beyond the range of the calculator. This error does not
occur during graphing. The TI
.
82 allows for undefined values
on a graph.
RESERVED
You are attempting to use a system variable inappropriately.
See Appendix A.
SIGN CHNG
The
solve(
function did not detect a sign change. Examine a
graph of the function. If the equation has a solution, change
the bounds and/or the initial guess.
SINGULAR MAT
¦
A singular matrix (determinate = 0) is not valid as the
argument for
-1
.
¦
You are attempting a polynomial regression with lists that
are not appropriate
This error does not occur during graphing. The TI
.
82 allows
for undefined values on a graph.
B-10 Reference Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/09/01 9:46 AM Printed:
02/09/01 12:44 PM Page 10 of 12
SINGULARITY
expression
in the
solve(
function contains a singularity
(a point at which the function is not defined). Examine a
graph of the function. If the equation has a solution, change
the bounds and/or the initial guess.
STAT
You are attempting a stat calculation with lists that are not
appropriate.
¦
Statistical analyses must have at least two data points.
¦
Med
.
Med
must have at least three points in each partition.
¦
Freq
, when used, must be an integer
‚
0
.
¦
(Xmax
N
Xmin)
à
Xscl
must be
47 for a histogram.
STAT PLOT
You are trying to display a graph when there is a
StatPlot On
that uses an undefined list.
SYNTAX
The command contains a syntax error. Look for misplaced
functions, arguments, parentheses, or commas. See Appendix
A and the appropriate chapter.
TOL NOT MET
The algorithm cannot return a result accurate to the
requested tolerance.
UNDEFINED
You are referencing a variable that is not currently defined;
for example, a stat variable when there is no current
calculation because a list has been edited or when the
v
ariable is not valid for the current calculation, such as
a
after
Med
.
Med
.
WINDOW RANGE
There is a problem with the
WINDOW
variables.
¦
You may have defined
Xmax
Xmin
,
Ymax
Ymin
,
q
max
q
min
and
q
step
>
0
(or vice versa),
Tstep
=
0
, or
Tmax
Tmin
and
Tstep
>
0
(or vice versa).
¦
WINDOW
variables are too small or too large to graph
correctly, which can occur if you attempt to zoom in or out
so far that you are not within the numerical range of the
calculator.
ZOOM
A point or a line, rather than a box, is defined in
ZBox
or a
math error resulted from a
ZOOM
operation.
Reference Information B-11
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:
02/27/01 12:25 PM Page 11 of 13
Support and Service Information
Product Support
Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands
For general questions, contact Texas Instruments Customer Support:
phone:
1
.
800
.
TI
.
CARES (1
.
800
.
842
.
2737)
e-mail:
ti-cares@ti.com
For technical questions, call the Programming Assistance Group of Customer Support:
phone:
1
.
972
.
917
.
8324
Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands
Contact TI by e-mail or visit the TI
Calculator
home page on the World Wide Web.
e-mail:
ti-cares@ti.com
Internet:
education.ti.com
Product Service
Customers in the U.S. and Canada Only
A
lways contact Texas Instruments Customer Support before returning a product for
service.
Customers outside the U.S. and Canada
Refer to the leaflet enclosed with this product or contact your local Texas
Instruments retailer/distributor.
Other TI Products and Services
V
isit the TI
Calculator
home page on the World Wide Web.
education.ti.com
B-12 Reference Information
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:
02/27/01 12:25 PM Page 12 of 13
Warranty Information
Customers in the U.S. and Canada Only
One-Year Limited Warranty for Electronic Product
This Texas Instruments (“TI”) electronic product warranty extends only to the original
purchaser and user of the product.
Warranty Duration.
This TI electronic product is warranted to the original purchaser
for a period of one (1) year from the original purchase date.
Warranty Coverage.
This TI electronic product is warranted against defective
materials and construction.
THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN
DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER
SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS
OR CONSTRUCTION.
Warranty Disclaimers.
ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE,
INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED
IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL
NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL
OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE
CONSUMER OR ANY OTHER USER.
Some states/provinces do not allow the exclusion or limitation of implied warranties or
consequential damages, so the above limitations or exclusions may not apply to you.
Legal Remedies.
This warranty gives you specific legal rights, and you may also have
other rights that vary from state to state or province to province.
Warranty Performance.
During the above one (1) year warranty period, your defective
product will be either repaired or replaced with a reconditioned model of an equivalent
quality (at TI’s option) when the product is returned, postage prepaid, to Texas
Instruments Service Facility. The warranty of the repaired or replacement unit will
continue for the warranty of the original unit or six (6) months, whichever is longer.
Other than the postage requirement, no charge will be made for such repair and/or
replacement. TI strongly recommends that you insure the product for value prior to
mailing.
Software.
Software is licensed, not sold. TI and its licensors do not warrant that the
software will be free from errors or meet your specific requirements.
All software is
provided “AS IS.”
Copyright.
The software and any documentation supplied with this product are
protected by copyright.
Reference Information B-13
8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:
02/27/01 12:25 PM Page 13 of 13
Australia & New Zealand Customers only
One-Year Limited Warranty for Commercial Electronic Product
This Texas Instruments electronic product warranty extends only to the
original purchaser and user of the product.
Warranty Duration.
This Texas Instruments electronic product is warranted
to the original purchaser for a period of one (1) year from the original
purchase date.
Warranty Coverage.
This Texas Instruments electronic product is warranted
against defective materials and construction. This warranty is void if the
product has been damaged by accident or unreasonable use, neglect, improper
service, or other causes not arising out of defects in materials or construction.
Warranty Disclaimers. Any implied warranties arising out of this sale,
including but not limited to the implied warranties of merchantability
and fitness for a particular purpose, are limited in duration to the
above one-year period. Texas Instruments shall not be liable for loss
of use of the product or other incidental or consequential costs,
expenses, or damages incurred by the consumer or any other user.
Some jurisdictions do not allow the exclusion or limitation of implied
warranties or consequential damages, so the above limitations or exclusions
may not apply to you.
Legal Remedies. This warranty gives you specific legal rights, and you may
also have other rights that vary from jurisdiction to jurisdiction.
Warranty Performance.
During the above one (1) year warranty period,
your defective product will be either repaired or replaced with a new or
reconditioned model of an equivalent quality (at TI’s option) when the product
is returned to the original point of purchase. The repaired or replacement unit
will continue for the warranty of the original unit or six (6) months, whichever
is longer. Other than your cost to return the product, no charge will be made
for such repair and/or replacement. TI strongly recommends that you insure
the product for value if you mail it.
Software.
Software is licensed, not sold. TI and its licensors do not warrant
that the software will be free from errors or meet your specific requirements.
All software is provided “AS IS.”
Copyright.
The software and any documentation supplied with this product
are protected by copyright.
All Customers Outside the U.S. and Canada
For information about the length and terms of the warranty, refer to your package
and/or to the warranty statement enclosed with this product, or contact your local Texas
Instruments retailer/distributor.
Index I-1
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 1 of 10
- A -
a
variable, 12-14 to 12-16, A-28
ã
A
ä
matrix, 10-4, 10-8, 10-9, A-28
abs
, 2-4, 10-10, A-2
Absolute value, 2-4, 10-10, A-2
Accuracy, 3-13, B-4, B-5
Addition:
+
, 2-3, 10-10, A-2
ALPHA
,
ALPHA-LOCK
, 1-8
and
, 2-16, A-2
Angle entry indicators (
¡
,
r
,
'
), 2-13
ANGLE
menu, 2-13, 2-14
Angle
MODE
, 1-11
Ans
, 1-16, 13-4
Antilogs, 2-4
APD, 1-2
Applications
Area between curves, 14-20
Box with lid, 6 to 13
Building height, 12-2 to 12-8
Buying a car, 14-5
Cobweb, 14-9
Compound interest, 4 to 5, 14-5
Family of curves, 13-2, 13-3
Ferris wheel, 14-12, 14-13
Forest and trees, 6-2
Fundamental theorem of calculus,
14-18, 14-19
Generating a sequence, 11-2
Graphing a circle, 3-2
Graphing inequalities, 14-6
Guess the coefficients, 14-10
Left-brain, right-brain test results,
14-2, 14-3
Lottery chances, 2-2
Path of a ball, 4-2
Polar rose, 5-2
Polynomial coefficients, 9-2
Predator-prey, 14-16, 14-17
Reservoir, 14-14, 14-15
Roots of a function, 7-6
Sending variables, 16-2
Shading a graph, 8-2
Sierpinski triangle, 14-8
Systems of linear equations, 10-2,
10-3
- A (Cont.) -
Applications (Cont.)
Systems of nonlinear equations,
14-7
Speeding tickets, 14-4
Unit circle and trig curves, 14-11
Arcsine, arcosine, arctangent.
See
sin
-1
,
cos
-1
,
tan
-1
ARGUMENT
error, B-6
Arrow keys, 1-8
augment(
, 10-12, 10-14, A-2
Automatic Power Down™, 1-2
Axes (graphing), 3-10
AxesOff
,
AxesOn
FORMAT
, 3-10, A-2
- B -
b
variable, 12-14 to 12-16, A-28
ã
B
ä
matrix, 10-4, 10-8, 10-9, A-28
Backup
, 16-8
BAD GUESS
error, B-6
Batteries, B-2
Boolean operators, 2-16
BOUND
error, B-6
Bounding a solution, 2-8, 3-23
BOX
(
VARS
) menu, 1-19, 12-14
Box
plot, 12-19 to 12-22
Break, 1-7, 13-4, B-6
BREAK
error, B-6
Busy indicator, 1-5, B-3
- C -
c
variable, 12-14 to 12-16, A-28
ã
C
ä
matrix, 10-4, 10-8, 10-9, A-28
Cable, 16-3
CALC
,
CALCULATE
, 13, 3-21 to 3-24,
4-6, 5-6, 6-6, 9-3
CALC
menu, 3-21 to 3-24
Calculus, 2-7, 3-24
Calling other programs, 13-11, 13-18
Cancelling a menu, 2, 1-17
Check Ram
screen, 15-2
Circle(
, 8-3, 8-9, A-2
Circles, 3-2, 8-9
Clearing, 1-8
cursor coordinates, 3-13
Index
I-2 Index
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 2 of 10
- C (Cont.) -
Clearing (Cont.)
display, 1-8
drawing, 8-16
expression, 1-8
Home screen, 1-8
list, 12-10 to 12-12
matrix, 10-6, 10-7
menu, 2, 1-17
table, 7-6
ClrDraw
, 3-24, 8-3, 8-16, A-2
ClrHome
, 13-13, 13-15, 13-17, A-3
ClrList
, 12-12, A-3
ClrTable
, 7-6, 13-13, 13-17, A-3
Cobweb graph.
See
Web
Coefficients (regression equation),
12-13 to 12-15
Combinations (probability), 2-12
Commands, 1-6, 13-4 to 13-6
Communications, 16-1 to 16-8
Compare, 2-16
Concatenating commands, 1-6, 1-14
Connected
MODE
, 1-9, 1-11, 3-4, A-3
Contrast setting, 3, 1-3
Conversions
fractions, 2-5, 11-2, A-8
polar to rectangular, 2-13, 2-14, A-15
rectangular to polar, 2-13, 2-14, A-17
Coordinates, 3-10
CoordOff
,
CoordOn
FORMAT
, 3-10, A-3
Correlation coefficient
r
, 12-14, 12-15,
A-28
cos
,
cos
–1
, 2-3, A-3, B-5
Cosine, 2-3, A-3, B-5
cosh
,
cosh
–1
, 2-11, A-3, B-5
CTL
(
PRGM
) menu, 13-7 to 13-12
Cube:
3
, 2-5, 2-6, 10-11, A-3
Cube root:
3
‡
, 2-5, 2-6, A-3
CubicReg
, 12-13, 12-15, A-4
Cubic fit/regression, 12-15
Cursor coordinates, 3-10
Cursor keys, 1-8
Cursors, 1-5, 1-8, B-3
Curve fitting, 12-4 to 12-8
- D -
d
variable, 12-14, 12-15, A-28
ã
D
ä
matrix, 10-4, 10-8, 10-9, A-28
DATA TYPE
error, B-6
8
Dec
, 2-5, A-4
Decimal display, 1-10, 2-5, A-4
Decimal
WINDOW
, 3-16, 3-18, A-21
Decrement and skip, 13-10
Definite integral, 2-5, 2-7, A-7, B-4, B-6
Degree/minute/second, 2-13, 2-14, A-5
Degree
MODE
, 1-9, 1-11, 2-13, 3-4, A-4
Degree notation
¡
, 2-13, A-4
Deleting, 1-8, 15-3
@
Tbl
variable, 7-2, 7-3, 7-6
@
X
,
@
Y
, 3-9, 3-18, A-28, B-4
DependAsk
, 7-3, 7-5, A-4
DependAuto
, 7-3, 7-5, A-4
Dependent variable, 7-3 to 7-5
Derivative.
See
Numerical derivative
det
, 10-12, A-4
Determinate, 10-12, A-4
Differentiation, 2-5, 2-6, 3-21, 3-24, 4-6,
5-6, A-12
dim
, 10-12, 10-13, 11-6, 11-7, A-4
Dimension (list), 11-6, 11-7, A-4
Dimension (matrix), 10-4 to 10-6, 10-12,
10-13, A-4
DIM MISMATCH
error, B-6
Disp
, 13-10, 13-13, 13-14, A-4
DispGraph
, 12-22, 13-10, 13-13, 13-15,
A-4
Display, 1-3 to 1-4
contrast, 3, 1-3, B-3
cursors, 1-5, 1-8, B-3
decimal, 2-5, A-4
DMS, 2-13, 2-14, A-5
fraction, 2-5, 11-2, A-8
graph, 3-11, 3-12
Home screen, 1-4
text, 8-3, 8-10, 9-4, 13-13, 13-15, A-13,
A-20
DispTable
, 13-10, 13-13, 13-15, A-4
DIVIDE BY 0
error, B-7
Division:
à
, 2-3, A-5
Index I-3
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 3 of 10
- D (Cont.) -
8
DMS
, 2-13, 2-14, A-5
DOMAIN
error, B-7
Dot
MODE
, 1-9, 1-11, 3-4, A-5
DRAW
menu, 8-3 to 8-11
Drawing
DrawF
, 8-7, A-5
function, 8-7
inverse function, 8-7
lines, 8-4 tfo 8-6
on a graph, 8-1 to 8-16
pixels, 8-13
points, 8-12
stat data, 12-6 to 12-8, 12-18 to 12-22
tangents, 8-6
DrawInv
, 8-7, A-5, B-8
DS<(
, 13-7, 13-10, A-5
Duplicate Name
message, 16-7, B-7
dy/dx
,
dy/dt
,
dx/dt
,
dr/d
q
, 3-21, 3-24,
4-6, 5-6
- E -
H
, 2-7, 3-24
e
variable, 12-14, 12-15, A-28
ã
E
ä
matrix, 10-4, 10-8, 10-9, A-28
e^
, 2-4, A-5, B-5
e
(natural log), 2-4
Edit keys, 1-8
Editors, 1-8, 9-3
function, 3-5, 3-6, 4-3, 5-3, 6-3
list, 9-3, 12-9 to 12-11
matrix, 10-4 to 10-6
program, 9-3
statistics, 9-3
table, 9-3
Y=
, 9-3
Element
list, 11-3 to 11-5
matrix, 10-4 to 10-9
sequence, 6-5
Else
, 13-7 to 13-9, A-5
End
, 13-7 to 13-9, A-5, B-8
Eng
MODE
, 1-9, 1-10, A-5
Engineering display, 1-9, 1-10, A-5
- E (Cont.) -
Entering
expressions, 1-6
functions, 1-7, 1-19, 3-5 to 3-7, 4-3,
5-3, 6-3, 7-4, A-28
lists, 11-2 to 11-5, 12-10 to 12-12
matrices, 10-4 to 10-9
negative numbers, 1-21, 2-4, 10-10,
A-12
programs, 13-4 to 13-6
statistics, 9-3, 12-2, 12-9
EOS, 1-20, 1-21, 2-15
EQ
(
VARS
) menu, 1-19, 12-14
Equal:
=
, 2-15, 10-11, A-5
Equation Operating System, 1-20, 1-21,
2-15
Equations, parametric, 4-2 to 4-6
Equations, solving, 2-5, 2-8, 3-22, A-18,
A-19, B-4, B-6, B-8, B-9
Erasing a program, 13-6, 15-3
Error in Xmit
message, B-7
Errors, 1-22, 11-5, 13-4, 16-6, B-3 to B-9
Evaluating expressions, 1-6
Evaluating functions, 3-21
Exclusive or, 2-16, A-21
Executing programs, 13-5
Exponent:
E
, 1-7, A-6
Exponential regression, 12-13, 12-16,
A-6
ExpReg
, 12-13, 12-16, A-6
Expressions, x, 1-6
- F -
‰
f(x)dx
, 3-21, 3-24, B-4
Factorial:
!
, 2-12, A-6, B-5
Family of curves, 3-12, 13-2, 13-3
Fill(
, 10-13, 11-6, 11-8, A-6
Fix
MODE
, 1-9, 1-10, A-6
Float
MODE
, 1-9, 1-10, A-6
fMax(
, 2-5, 2-6, A-6, B-4, B-6
fMin(
, 2-5, 2-6, A-7, B-4, B-6
fnInt(
, 2-5, 2-7, A-7, B-4, B-6
FnOff
,
FnOn
, 3-7, A-7
I-4 Index
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 4 of 10
- F (Cont.) -
For(
, 13-7 to 13-9, A-7, B-8
FORMAT
.
See
WINDOW
fPart
, 2-9, 10-11, A-7, A-8
Fractional part, 2-9, 10-11, A-7, A-8
Fractions, 2-5
8
Frac
, 2-5, 11-2, A-8
Free-moving cursor, 3-13, 4-6, 5-6, 6-4
Freq
(frequency), 12-20
Friendly
WINDOW
(
ZDecimal
), 3-16,
3-18, A-21
FullScreen
, 1-9, 1-11, 9-4, A-8
Func
MODE
, 1-9, 1-11, 3-4, 8-7, A-8
Functions, x, 1-6, 1-7
defining, 3-5, 3-6, 4-3
evaluating, 3-6, 3-21
graphing, 3-1 to 3-22
integral, 2-5, 2-7, 3-21, 3-24, A-7, B-4,
B-6
maximum, 2-5, 2-6, A-6, B-4, B-6
minimum, 2-5, 2-6, A-7, B-4, B-6
parametric, 4-2 to 4-4
polar, 5-2 to 5-4
sequence, 6-2 to 6-4
selecting, 3-7, 4-3, 5-3, 6-4
- G -
GDB
n
variables, 1-19, A-28
Get(
, 13-13, 13-17, A-8
getKey
, 13-13, 13-16, A-8
Getting Started.
See
Applications
Glossary, x
Goto
, 13-7, 13-10, A-8, B-8
Graph
accuracy, 3-11
database, 1-19, 8-15
defining, 3-3, 4-3, 5-3, 6-3
displaying, 3-11, 3-12, 4-3, 5-3, 6-3,
9-3
FORMAT
, 3-10, 9-3
MODE
, 1-10
parametric, 4-1 to 4-6
picture, 8-14
polar, 5-1 to 5-6
sequence, 6-1 to 6-6
WINDOW
, 10, 1-19, 3-8 to 3-9, 3-16 to
3-20, 4-3 to 4-6, 5-4 to 5-6, 6-4 to
6-6, 12-21, 13-15, A-28, B-8
- G (Cont.) -
Greater than:
>
, 2-15, A-8
Greater than or equal:
‚
, 2-15, A-8
Greatest integer, 2-9, 2-10, 10-11
GridOff
,
GridOn
FORMAT
, 3-10, A-8
Guess, 2-8, 3-22, 3-23, B-6
Guidebook, using, viii, ix
- H -
Histogram
, 12-19 to 12-22, B-9
Home screen, x, 1-4, 9-3
Horizontal
, 8-3, 8-5, A-8
Horizontal line, 8-5
HYP
(
MATH
) menu, 2-11
Hyperbolic functions, 2-11
Hyperbolic arcsine, arcosine,
arctangent.
See
sinh
-1
,
cosh
-1
,
tanh
-1
- I -
identity
(matrix), 10-12, 10-13, A-8
If
, 13-7, 13-8, A-9, B-8
ILLEGAL NEST
error, B-7
Implied multiplication, 1-21
Increment and skip, 13-10
INCREMENT
error, B-7
Independent variable, 3-5, 7-3, 7-5
IndpntAsk
, 7-3, 7-5, A-9
IndpntAuto
, 7-3, 7-5, A-9
Inequalities, graphing, 14-6
Input
, 13-13, A-9
Input to programs, 13-13 to 13-17
INPUT/OUTPUT
, 13-13 to 13-17
Inserting, 1-8
Instructions, x, 1-6, 1-7
int
, 2-9, 2-10, 10-11, A-9
Integer part, 2-9, 2-10, 10-11, A-9
Integrals, 2-5, 2-7, 3-21, 3-24, A-7, B-4,
B-6
Intercepts, 3-21, 3-22, B-4
intersect
, 3-21, 3-23, B-4
Intersection, 3-21, 3-23, B-4
Interrupt, 1-7, 13-4
INVALID
error, B-7
INVALID DIM
error, B-7
Index I-5
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 5 of 10
- I (Cont.) -
Inverse:
–1
, 2-3, 10-11, A-9
hyperbolics, 2-11
functions, 8-3, A-5, B-8
logs, 2-4
matrices, 10-11
trigs, 2-3
iPart
, 2-9, 2-10, 10-11, A-9
IS>(
, 13-7, 13-10, A-9
ITERATIONS
error, B-7
- L -
L
n
(lists), 11-2 to 11-5, A-28
LABEL
error, B-8
LabelOff
,
LabelOn
, 3-10, A-10
Labels (graph), 3-10, A-10
Labels (program), 13-10
Last Answer
, 1-16, 13-4
Last Entry
, 1-14, 1-15, 13-4
Lbl
, 13-7, 13-10, A-10, B-8
Less than:
<
, 2-15, A-10
Less than or equal:
, 2-15, A-10
Line(
, 8-3, 8-4, A-10
Line (stat), 12-18, 12-20 to 12-22
Linear regression, 12-15, 12-16
LINK
, 16-1 to 16-8
LINK
menu, 16-2 to 16-8
LinReg
, 12-13, 12-15, 12-16, A-10
LIST MATH
menu, 11-9, 11-10
LIST OPS
menu, 11-6 to 11-8
Lists, x, 11-1 to 11-10
arguments, 2-3, 11-5
dimension, 11-6, 11-7, A-4
elements, 12-10 to 12-12
entering, 11-2 to 11-5, 12-10 to 12-12
graphing, 3-12, 11-5, 13-2, 13-3
variables, 11-2 to 11-5, A-28
viewing, 12-10
ln
, 2-4, A-10, B-5
LnReg
, 12-13, 12-16, A-10, A-11
log
, 2-4, A-11, B-5
Logic operations, 2-16
Logarithm, 2-4
Logarithmic regression, 12-16
LOGIC
menu, 2-16
Lower bound, 2-8, 3-23, B-6
- M -
Mark
(
STAT
), 12-20 12-22
MATH
menu, 2-2 to 2-12
Matrices, x, 9-3, 10-1 to 10-14
determinant, 10-12
dimensions, 10-4, 10-12, 10-13
elements, 10-4 to 10-9
entering, 10-4 to 10-9
inverse, 10-11
math, 10-10 to 10-14
row operations, 10-14
transpose, 10-12
variables, 10-4, 10-8, 10-9, A-28
viewing, 10-5
MATRIX EDIT
menu, 10-4
MATRX MATH
menu, 10-12 to 10-14
MATRX NAMES
menu, 10-8, 10-9
max(
, 2-9, 2-10, 11-9, A-11
maximum
(
CALC
), 3-21, 3-23, B-4
Maximum, 2-9, 2-10, 3-21, 3-23, 11-9,
12-14, 12-19, 12-21
maxX
,
maxY
, 12-14, 12-19, 12-21, A-28
mean(
, 11-9, A-11
Med
, 12-14, 12-19, 12-21, A-28
Med
.
Med
, 12-13, 12-15, A-11
median(
, 11-9, A-11
Median point, 12-19
Median-median line, 12-15
MEM
menu, 15-2 to 15-4
MEM
screens, 15-2, 15-3
MEMORY
error, B-8
Memory backup, 16-8
Memory full message, 16-7, B-3, B-8
Memory management, 15-1 to 15-4
Menu(
, 13-7, 13-11, A-11
Menu map, A-22 to A-27
Menus, x, 2, 1-17 to 1-19, 9-3
ANGLE
, 2-13, 2-14
BOX
(
VARS
), 1-19, 12-14
CALC
, 3-21 to 3-24
CTL
(
PRGM
), 13-7 to 13-12
DRAW
, 8-3 to 8-11
EQ
(
VARS
), 1-19, 12-14
HYP
(
MATH
), 2-11
I/O
(
PRGM
), 13-13 to 13-17
LINK
, 16-2 to 16-8
I-6 Index
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 6 of 10
- M (Cont.) -
Menus (Cont.)
LIST MATH
, 11-9, 11-10
LIST OPS
, 11-6 to 11-8
MATH
, 2-2 to 2-12
MATRX EDIT
, 10-4
MATRX MATH
, 10-12 to 10-14
MATRIX NAMES
, 10-8, 10-9
MEM
, 15-2 to 15-4
NUM
(
MATH
), 2-9, 2-10
POINTS
(
DRAW
), 8-12, 8-13
PRB
(
MATH
), 2-12
PRGM EXEC
, 13-5, 13-6
PRGM EDIT
, 13-5
PRGM NEW
, 13-5
PTS
(
VARS
), 1-19, 12-14
G
(
VARS
), 1-19, 12-14
STAT CALC
, 12-13 to 12-17
STAT EDIT
, 12-12
STAT MARK
, 12-22
STAT PLOTS
, 12-22
STAT TYPE
, 12-22
STO
(
DRAW
), 8-14, 8-15
TEST
, 2-15
TEST LOGIC
, 2-16
VARS
, 1-19, 3-8
WINDOW FORMAT
, 3-10
X/Y
(
VARS
), 1-19, 12-14
Y-VARS
, 1-19
ZOOM
, 3-16 to 3-18
ZOOM MEMORY
, 3-19 to 3-20, 4-6
min(
, 2-9, 2-10, 11-9, A-11
minimum
(
CALC
), 3-21, 3-23, B-4
Minimum, 2-9, 2-10, 3-21, 3-23, 11-9,
12-14, 12-19, 12-21
Minute notation:
'
, 2-13, A-12
minX
,
minY
, 12-14, 12-19, 12-21
MODE
, 1-9 to 1-11, 3-4, 4-3, 5-3, 9-3
MODE
error, B-8
Modeling, 12-4 to 12-8
Multiargument functions, 1-20
Multiple entries, 1-6, 1-14
Multiplication:
…
, 2-3, 10-10, A-12
- N -
n
(statistics), 12-14, A-28
n
(
Seq
), 6-5, 6-6, 7-3, A-28
Natural log, 2-4
nCr
, 2-12, A-12
nDeriv(
, 2-5, 2-7, A-12
Negation:
M
, 1-21, 2-4, 10-10, A-12
n
Max
,
n
Min
, 6-5, 6-6
Normal
MODE
, 1-9, 1-10, A-13
not
, 2-16, A-13
Not equal:
ƒ
, 2-15, 10-11, A-13
nPr
, 2-12, A-13
n
Start
, 6-6
NUM (MATH)
menu, 2-9, 2-10
Numerical derivative, 2-5, 2-6, 3-21,
3-24, 4-6, 5-6, A-12
Numerical integral, 2-5, 2-7, 3-21, 3-24,
A-7, B-4, B-6
- O -
OFF
,
ON
, 3, 1-2
1-Var Stats
, 12-13, 12-14, A-13, B-9
One-variable statistics, 12-13, 12-14,
B-9
or
, 2-16, A-13
Output(
, 9-4, 13-13, 13-15, A-13
OVERFLOW
error, B-8
- P -
Panning, 3-14, 4-6, 5-6, 6-6
Par
MODE
, 1-9, 1-11, 3-4, 4-3, A-14
Parametrics, 1-19, 4-1 to 4-6
Parentheses, 1-21
Pause
, 13-7, 13-10, 13-14, 13-15, 13-17,
A-14
Pausing a graph, 3-11
Pausing a program, 13-10
Pen
, 8-3, 8-11
Permutations, 2-12
Pi:
p
, 2-4
Piece-wise functions, graphing, 14-4
Pixel, 3-13, 8-12, 8-13, 9-4, A-15, B-4
Pic
n
(pictures), 1-19, 8-14, A-28
Plot
n
(
, 12-20, 12-22, A-14
PlotsOff
,
PlotsOn
, 12-21, A-14
Plotting graphs, 3-11, 3-12
Plotting stat data, 12-6 to 12-8, 12-18 to
12-22
Index I-7
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 7 of 10
- P (Cont.) -
POINTS (DRAW)
menu, 8-12, 8-13
Pol
MODE
, 1-9, 1-11, 3-4, 5-3, A-14
Polar coordinates, 3-10, 4-6, 5-6, 6-5,
A-14
Polar graphing, 1-19, 5-1 to 5-6
PolarGC
, 3-10, 4-6, 5-6, 6-5, A-14
Polar to rectangular, 2-13, 2-14, A-15
Polynomial fit/regression, 12-15
Power of ten:
10^
, 2-4, A-14, B-5
Power regression, 12-16
Powers:
^
, 2-3, 10-11, A-14
PRB (MATH)
menu, 2-12
prgm
, 13-7, 13-11, 13-18, A-14
PRGM CTL
menu, 13-7 to 13-12
PRGM EXEC
menu, 13-5, 13-6
PRGM EDIT
menu, 13-5
PRGM I/O
menu, 13-13 to 13-17
PRGM NEW
menu, 13-5
PrintScreen
, 13-13, 13-17, A-14
Probability, 2-2, 2-12
prod
, 11-9, 11-10, A-15
Product of a sequence, 11-10
PROGRAM
editor, 9-3
Programs, 13-1 to 13-18
commands, 13-4
executing programs, 13-5
names, 13-4
Prompt
, 13-13, 13-15, A-15
P
8
Rx(
,
P
8
Ry(
, 2-13, 2-14, A-15
Pt-Change(
, 8-12, A-15
Pt-Off(
,
Pt-On(
, 8-12, A-15
PTS
(
VARS
) menu, 1-19, 12-14
PwrReg
, 12-13, 12-16, A-15
Pxl-Change(
, 8-12, 8-13, 9-4, A-15
Pxl-Off(
,
Pxl-On(
, 8-12, 8-13, 9-4, A-15
pxl-Test(
, 8-12, 8-13, 9-4, A-15
- Q -
Q
1
,
Q
3
12-14, 12-19, 12-21, A-28
QuadReg
, 12-13, 12-15, A-15
Quadratic fit/regression, 12-15
Quartiles, 12-14, 12-19
QuartReg
, 12-13, 12-15, A-16
Quartic fit/regression, 12-15
QuickZoom, 3-14, 4-6, 5-6, 6-6
- R -
r
(radian notation), 2-13, A-16
r
(statistics), 12-14, 12-15, A-28
R
variable, 4-6, 5-5, 5-6, A-28
r
n
functions, 1-19, 5-3, A-28
Radian
, 1-9, 1-11, 2-13, 3-4, A-16
rand
, 2-12, A-16
randM(
, 10-12, 10-13, 16-2, A-16
Random numbers, 2-12, 10-12, 10-13,
16-2, A-16
RANGE
.
See
WINDOW
RCL
, 1-13, 13-6
RclWindow
, 16-4, 16-5
RecallGDB
, 8-15, A-16
Recalling, 1-13, 8-14, 8-15, 13-6
RecallPic
, 8-14, A-16
Rectangular coodinates, 3-10, 4-6, 5-6,
6-5, A-16
Rectangular to polar, 2-13, 2-14, A-17
RectGC
, 3-10, 4-6, 5-6, 6-5, A-16
RegEQ
(regression equation), 12-4 to
12-8, 12-14, A-28, B-4
Regressions, 12-4 to 12-8
Relational operators, 2-15, 10-11
Repeat
, 13-7, 13-9, A-16, B-8
RESERVED
error, B-8
Reserved variables, A-28, B-8
Resetting, 3, 15-4
Residuals, 12-2 to 12-8
Return
, 13-7, 13-12, A-16
root
x
‡
, 2-5, 2-6, A-16
root, 3-21, 3-22, B-4
Root of a function, 3-21, 3-22, B-4
round(
, 2-9, 10-11, A-16, A-17
Row operations (matrices), 10-2, 10-3,
10-12, 10-14
rowSwap(
, 10-12, 10-14, A-17
row+(
,
…
row(
,
…
row+(
, 10-2, 10-3, 10-12,
10-14, A-17
Running programs, 13-5
R
8
Pr(
,
R
8
P
q
(
, 2-13, 2-14, A-17
I-8 Index
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 8 of 10
- S -
Scatter
plot, 12-18, 12-20 to 12-22
Sci
MODE
, 1-7, 1-9, 1-10, A-17
Scientific notation, 1-7, 1-9, 1-10, A-17
2nd
, 1-8
SELECT
(
LINK
) screen, 16-5
SelectAll+
,
SelectAll-
, 16-5
SelectCurrent
, 16-5
Selecting from a menu, 2, 1-17
Selecting functions, 1-19
Send(
, 13-13, 13-17, A-17
Sending, 16-1 to 16-8
Seq
, 1-9, 1-11, 3-4, 6-3, 7-3, A-17
seq(
, 6-5, 11-2, 11-6, 11-8, 11-10, A-17,
B-7
Sequence
generating, 6-5, 11-2, 11-6, 11-8,
11-10, A-17
graphing, 1-19, 6-1 to 6-6
product, 11-10
sum, 11-10
Sequential
, 1-9, 1-11, 3-4, A-17
Series, 6-5, 11-10
SET UP CALCS
, 9-3, 12-13, 12-17
Shade(
, 8-2, 8-3, 8-8, A-18
SIGN CHNG
error, B-8
s
x
,
s
y
, 12-14, A-28
G
(
VARS
) menu, 1-19, 12-14
G
x
,
G
y
,
G
x
2
,
G
y
2
,
G
xy
, 12-14, A-28
Simul
, 1-9, 1-11, 3-4, 3-12, A-18
sin
,
sin
–1
, 2-3, A-18, B-5
Sine, 2-3, A-18, B-5
SINGULAR MAT
error, B-8
SINGULARITY
error, B-9
sinh
,
sinh
–1
, 2-11, A-18, B-5
Smart Graph, 3-11, 3-24, 4-5, 5-5, 6-5
solve(
, 2-5, 2-8, 3-22, A-18, A-19, B-4,
B-6 to B-9
Solving equations, 2-5, 2-8, 3-22, A-18,
A-19, B-4, B-6 to B-9
SortA(
, 11-6, 12-12, 12-18, A-19
SortD(
, 11-6, 12-12, 12-18, A-19
Sorting lists, 11-6, 12-3, 12-12
- S (Cont.) -
Split
, 1-9, 1-11, 9-4, A-19
Split screen, 9-1 to 9-4, 8-10, 8-13, 13-15
Square:
2
, 2-3, 10-11, A-19
Square root:
‡
, 2-3, A-19, B-5
Standard deviation, 12-14
Square
WINDOW
, 3-2, 3-16, 3-18, A-21
Standard
WINDOW
, 3-8, 3-16, 3-18, 4-6,
5-6, A-21
STAT
error, B-9
STAT CALC
menu, 12-13 to 12-17
STAT EDIT
menu, 12-12
STAT
list editor, 9-3, 12-9 to 12-12
STAT MARK
menu, 12-22
STAT PLOT
error, B-9
STAT PLOTS
, 9-3, 12-20, 12-22
STAT TYPE
menu, 12-22
Statistics, 1-19, 12-1 to 12-22
analysis, 12-2 to 12-9, 12-13 to 12-22
calculations, 12-2 to 12-9, 12-13 to
12-17
data, 12-9 to 12-11
plotting, 12-6 to 12-8, 12-18 to 12-22
results, 1-19, 12-4, 12-5
variables, 1-19, 12-4, 12-5
Step-wise functions, graphing, 14-4
STO (DRAW)
menu, 8-14, 8-15
Stop
, 13-7, 13-12, A-19
Stopping, 1-7, 3-11, 13-4, 13-12
Store:
!
, 1-13, 11-3, A-19
StoreGDB
, 8-15, A-19
StorePic
, 8-14, A-19
Storing, 1-13, 8-14, 8-15
Subroutines, 13-10, 13-18
Subtraction:
–
, 2-3, 10-10, A-19, A-20
sum
, 11-9, 11-10, A-20
Sum of a sequence, 11-10
Summation, 11-10
Sx
,
Sy
, 12-14, A-28
SYNTAX
error, B-9
System variables, A-28
Index I-9
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 9 of 10
- T -
T
(transpose), 10-12, A-20
T
variable, 4-5, 4-6, 7-3, A-28
Tables, 7 to 9, 7-1 to 7-6
TABLE SETUP
screen, 7-2, 7-3, 9-3
Table variables, 1-19
tan
,
tan
–1
, 2-3, A-20, B-5
Tangent(
, 8-3, 8-6, A-20
Tangent line, 8-6
tanh
,
tanh
–1
, 2-11, A-20, B-5
TblMin
, 1-19, 7-2, 7-3, 7-5, 12-4, 12-5
TEST
menu, 2-15
TEST LOGIC
menu, 2-16
Text(
, 8-3, 8-10, 9-4, A-20
Then
, 13-7, 13-8, A-20
q
variable, 4-6, 5-5, 5-6, 7-3, A-28
q
max
,
q
min
, 5-4, 5-5, 5-6, B-4, B-9
q
step
, 5-4, 5-5, 5-6, B-4, B-9
Time
FORMAT
, 6-4 to 6-6, A-20
Tmax
,
Tmin
, 4-4, 4-5, B-4, B-9
TOL NOT MET
error, B-9
Tolerance, 2-6, 2-7, 3-23, 3-24
Trace
, 3-15, A-20
TRACE
, 11, 3-14, 3-15, 4-6, 5-6, 6-5, 9-3,
12-21
Transmitting, 16-1 to 16-8
Transpose:
T
, 10-12, A-20
Trig functions, 2-3
Tstep
, 4-4, 4-5, B-4, B-9
Turning functions on and off, 1-19
Turning the TI
.
82 on and off, 1-2
2-Var Stats
, 12-13, 12-14, A-21
Two-variable statistics, 12-13, 12-14
- U -
U
n
,
U
n
-1
, 1-19, 6-2 to 6-6, 11-8, A-28
UNDEFINED
error, B-9
U
n
Start
, 6-4, 6-6, A-28
Upper bound, 2-8, 3-23, B-6
- V -
value
, 3-21, 4-6, 5-6
Variables, x, 1-12, 1-13, A-28
VARS
menu, 1-19, 3-9
Vertical
, 8-3, 8-5, A-21
Vertical line, 8-5
Viewing rectangle, viewing window.
See
WINDOW
V
n
,
V
n
-1
, 1-19, 6-2 to 6-6, 11-8, A-28
V
n
Start
, 6-6, A-28
- W -
WARNING Memory Backup
message,
16-8
Web
FORMAT
, 6-5, 6-6, A-21
While
, 13-7, 13-9, A-21, B-8
WINDOW
, 10, 1-19, 3-8 to 3-9, 3-16 to
3-20, 4-3 to 4-6, 5-4 to 5-6, 6-4 to
6-6, 12-21, 13-15, A-28, B-8
WINDOW FORMAT
, 3-10, 9-3
WINDOW RANGE
error, B-9
- X -
X
,
T
,
q
key, 3-5, 4-3, 5-3
X
, 3-5, 4-5, 4-6, 5-5, 5-6, 6-5, 6-6, 7-3,
A-28, B-4
v
, 12-14, A-28
x
1
,
x
2
,
x
3
, 12-14, 12-15, A-28
X
n
T
functions, 1-19, 4-3, A-28
XFact
variable, 3-17, 3-19, 3-20
Xlist
, 12-20
Xmax
,
Xmin
,
Xscl
, 3-8, 3-13, 3-18, 4-4, 4-
6, 5-4, 5-6, 6-4, 6-6, 12-19, 13
.
15,
A-28, B-4, B-9
xor
, 2-16, A-21
X/Y
(
VARS
) menu, 1-19, 12-14
xyLine
, 12-18, 12-20 to 12-22
I-10 Index
8299INDX.DOC TI-82, Index, English Bob Fedorisko Revised: 02/09/01 11:35 AM Printed: 02/09/01
12:44 PM Page 10 of 10
- Y -
w
, 12-14, A-28
Y
, 3-8, 4-5, 4-6, 5-5, 5-6, 6-5, 6-6, A-28,
B-4
Y-VARS
menu, 1-19
Y
n
, 1-19, 3-5 to 3-7, 13-15, A-28
y
1
,
y
2
,
y
3
, 12-14, 12-15, A-28
Y
n
T
functions, 1-19, A-28
Y=
editor, 1-19, 3-5 to 3-7, 4-3, 5-3, 6-3,
7-4, A-28
Y=
functions.
See
Y
n
,
r
n
X
n
T
,
U
n
functions
YFact
variable, 3-17, 3-19, 3-20
Ylist
, 12-20
Ymax
,
Ymin
,
Yscl
, 3-8, 3-13, 3-18, 4-4,
4-6, 5-4, 5-6, 6-4, 6-6, 12-19,
13
.
15, A-28, B-4, B-9
- Z -
ZBox
, 3-16, A-21
ZDecimal
, 3-16, 3-18, A-21
Zero of a function, 3-21, 3-22, B-4
ZInteger
, 3-16, 3-18, A-21
ZOOM
, 12, 1-19, 3-16 to 3-20, 4-6, 9-3
ZOOM
error, B-9
ZOOM FACTORS
, 3-17, 3-19, 3-20
ZOOM MEMORY
, 3-19 to 3-20, 4-6
ZOOM
menu, 3-16 to 3-18
Zoom In
, 3-16, 3-17, 3-20, A-21
Zoom Out
, 3-16, 3-17, 3-20, A-21
ZoomRcl
, 3-19, 4-6, 5-6, A-21
ZoomSto
, 3-19, 4-6, 5-6, A-21
ZoomStat
, 3-16, 3-18, 12-19, 12-21, A-21
ZPrevious
, 3-19, A-21
ZSquare
, 3-2, 3-16, 3-18, 5-2, A-21
ZStandard
, 3-16, 3-18, 4-6, 5-6, A-21
ZTrig
, 3-16, 3-18, A-21
Z
q
max
,
Z
q
min
,
Z
q
step
, 5-6, A-28
ZTmax
,
ZTmin
,
ZTstep
, 4-6, A-28
Z
n
Max
,
Z
n
Min
,
Z
n
Start
, 6-6, A-28
ZU
n
Start
,
ZV
n
Start
, 6-6, A-28
ZXmax
,
ZXmin
,
ZXscl
, 3-19, A-28
ZYmax
,
ZYmin
,
ZYscl
, 3-19, A-28
@
Tbl
, 7-2, 7-3, 7-6
@
X
,
@
Y
, 3-9, 3-18, A-28, B-4
H
, 2-7, 3-24
s
x
,
s
y
, 12-14, A-28
G
(
VARS
) menu, 1-19, 12-14
G
x
,
G
y
,
G
x
2
,
G
y
2
,
G
xy
, 12-14, A-28
q
, 4-6, 5-5, 5-6, 7-3, A-28
q
max
,
q
min
, 5-4, 5-5, 5-6, B-4, B-9
q
step
, 5-4, 5-5, 5-6, B-4, B-9
… 259 …


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