Texas Instruments TI-73, TI-73 EXPLORER User Manual 2

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In this guidebook, TI-73 refers to both the TI-73 and TI-73 Explorer. All functions, instructions, and examples in this guidebook work identically for both the TI-73 and the TI-73 Explorer.

Macintosh is a registered trademark of Apple Computer, Inc.

Important Information

Texas Instruments makes no warranty, either express 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 calculator. 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.

This digital apparatus does not exceed the Class B limits for radio noise emissions from digital apparatus set out in the Radio Interference Regulations of the Canadian Department of Communications.

Table of ContentsTable of Contents

Chapter 1: Operating the TIN73 1

Preparing to Use Your TIN73.........................................3

The Home Screen........................................................... 5

Entering Numbers and Other Characters ..................... 6

Functions and Instructions ..........................................12

Entering Expressions.................................................... 15

Retrieving Previous Entries - £ ......................17

Recalling and Storing the Last Answer - ¢ ......18

Mode Settings.............................................................. 22

Chapter 2: Math Operations 25

Keyboard Math Operations ........................................27

The 1 MATH Menu ................................................ 34

The 1 NUM Menu .................................................. 44

The 1 PRB Menu ....................................................49

The 1 LOG Menu.................................................... 54

Chapter 3: Fractions 57

Entering Fractions........................................................ 58

Using Fractions in Calculations ...................................59

Fraction Modes ............................................................60

Converting between Fractions and Decimals............. 64

Converting between Mixed Numbers and

Simple Fractions......................................................65

Chapter 4: Measurement Conversions and Constant Calculations 67

The - ‚ CONVERSIONS Menu.......................68

Constants...................................................................... 71

Chapter 5: Lists 77

Steps for Creating a List ..............................................78

The List Editor 3 ....................................................79

Naming a List ...............................................................79

Entering List Elements ................................................. 81

Editing Lists in the List Editor...................................... 87

The - v Ls Menu .................................................91

The - v OPS Menu ..............................................92

List Commands from the Home Screen .................... 102

TIN73 Table of Contents

Chapter 6: Statistical Plots 107

Steps for Defining a Stat Plot ................................... 108

Defining Statistical Data in Lists ............................... 109

Deselecting Y

Defining a Stat Plot ................................................... 109

Selecting Stat Plot Types ........................................... 111

Defining Stat Plot Options........................................ 112

Adjusting Window Values and Format .................... 114

Displaying the Stat Plot............................................. 114

Stat Plot Examples ..................................................... 114

Chapter 7: Statistical Analyses 127

The - v MATH Menu........................................ 128

The - v CALC Menu.......................................... 133

Chapter 8: Tables 149

What Is a Table? ........................................................ 150

Steps for Creating a Table ........................................ 151

Defining and Selecting Functions in the

Y= Editor &........................................................ 152

Setting Up the Table - f ............................ 153

Displaying the Table - i............................... 154

Table Setup from the Home Screen ......................... 161

Functions .......................................... 109

Chapter 9: Function Graphing 163

Steps for Graphing a Function.................................. 164

Example of Function Graphing................................. 165

Defining Functions in the Y= Editor & ................. 167

Selecting a Graph Style ............................................. 169

Setting the Window Format - g................ 171

Defining Window Values .......................................... 173

Displaying a Graph *....................................... 177

Adjusting Window Values with

the ( ZOOM Menu ........................................ 181

The ( MEMORY Menu........................................ 185

Chapter 10: Drawing 187

The 2 DRAW Menu ............................................. 188

The 2 POINTS Menu............................................ 201

The 2 STO Menu ................................................. 206

TIN73 Table of Contents

Chapter 11: Trigonometry 209

The - u TRIG Menu ........................................... 210

Graphing Trig Functions............................................ 214

The - u ANGLE Menu ....................................... 215

Chapter 12: Programming 221

What Is a Program? ...................................................223

Steps for Creating a Program.................................... 223

Creating and Naming a New Program .....................224

Entering Program Commands...................................226

The 8 CTL Menu ..................................................227

The 8 I/O Menu.................................................... 241

Editing Program Commands .....................................248

Executing a Program .................................................251

Debugging a Program............................................... 252

Chapter 13: Communication Link and the CBLàCBR Application 253

TIN73 Link Capabilities...............................................254

The Link SEND Menu 9 1 ................................... 255

The Link RECEIVE Menu 9 1 "..........................257

Transmitting Data Items............................................258

Backing Up Memory ..................................................261

Upgrading your TIN73 Graph Explorer Software.....262

The APPLICATIONS Menu 9............................... 263

Steps for Running the CBLàCBR Application .......... 264

Selecting the CBL/CBR Application ...........................265

Specifying the Data Collection Method ...................265

Specifiying Data Collection Options......................... 266

Collecting the Data.................................................... 273

Stopping Data Collection ..........................................274

Chapter 14: Memory Management 275

The - Ÿ MEMORY Menu................................... 276

Appendix A: Function and Instruction Reference 283

TI-73 Table of Contents

Appendix B: Reference Information 319

The TIN73 Menu Map ................................................ 320

The VARS Menu -

Equation Operating System (EOS é)........................ 330

In Case of Difficulty ................................................... 330

Correcting an Error.................................................... 331

Error Messages........................................................... 332

Appendix C: BatteryàService and Warranty Information 339

Battery Information .................................................. 340

Texas Instruments (TI) Support and Service ............. 342

Warranty Information............................................... 343

Index 345

}

....................................... 329

Operating the Operating the

TITIN

7373

Preparing to Use Your TIN73................................................. 3

Installing the AAA Batteries........................................... 3

Turning the TIN73 On and Off .......................................3

Adjusting the Display Contrast ......................................4

Resetting Memory and All Defaults............................... 4

The Home Screen................................................................... 5

Entering Numbers and Other Characters.............................6

Entering a Negative Number a................................... 6

Entering a Number in Scientific Notation - {....... 7

Entering Secondary Functions -...............................7

Entering Text - t................................................. 7

Common Display Cursors ..............................................10

Editing Numbers and Characters .................................11

Functions and Instructions ..................................................12

Accessing Functions and Instructions from Menus .....12

Accessing FunctionsàInstructions from the CATALOG... 14

Entering Expressions............................................................15

Grouping Parts of Expressions with Parentheses ........16

Using Implied Multiplication in Expressions................ 16

Entering Multiple Expressions on One Line ................16

Retrieving Previous Entries - £..............................17

Recalling and Storing the Last Answer - ¢.............. 18

Continuing a Calculation with Ans .............................. 18

Using Ans as a Variable in an Expression ....................19

Storing Values to a Variable X ............................. 20

Recalling Variable Values - P .............................21

Chapter 1: Operating the TIN73

Mode Settings ..................................................................... 22

Numeric Notation Mode .............................................. 23

Decimal Notation Mode ............................................... 24

Angle Mode .................................................................. 24

Display Format Mode ................................................... 24

Simplification Mode ..................................................... 24

Chapter 1: Operating the TIN73

Preparing to Use Your

Before using your TIN73, you must install the batteries, turn on the calculator, and adjust the contrast. You may reset (clear) the calculator memory and defaults, if desired.

TIN

Installing the AAA BatteriesInstalling the AAA Batteries

Install four AAA batteries in the battery compartment on the back of the calculator. Arrange the batteries according to the polarity (+ and -) diagram in the battery compartment. For more information about installing batteries, see Appendix C: BatteryàService and Warranty Information.

Turning the Turning the

To turn on the TIN73, press ^.

To turn off the TIN73 manually, press the yellow - key and then press ^ (indicated in this book as - ).

When you press - , all settings and memory contents are retained by Constant Memoryè. Any error condition is cleared. To prolong battery life, the APDè (Automatic Power Down) feature turns the TIN73 off automatically after a few minutes without any activity.

TITIN

7373

On and Off On and Off

When you turn on the calculator:

• The Home screen is displayed if you previously turned off

the calculator by pressing - . It appears as it did

when you last used it; all errors are cleared.

 or 

• The calculator displays the last screen (including the

display, cursor, and any errors) that was displayed before

Automatic Power Down turned off the calculator.

Chapter 1: Operating the TIN73

Adjusting the Display ContrastAdjusting the Display Contrast

The brightness and contrast of the display can depend on room lighting, battery freshness, and viewing angle.

To adjust the contrast:

1. Press and release the yellow - key.

2. Press and hold $ (to darken the screen) or # (to lighten

the screen).

As you change the contrast setting, a number from 0 (lightest) to 9 (darkest) in the top-right corner indicates the current setting. You may not be able to see the number if the contrast is too light or too dark.

Resetting Memory and All DefaultsResetting Memory and All Defaults

Follow these steps to reset the TIN73 to its factory settings and clear all memory:

1. Turn on the calculator.

The ^ key

2. Display the

-Ÿ (above _ )

3. Display the

4. Display the menu.

MEMORY

RESET

RESET RAM

menu.

Chapter 1: Operating the TIN73

5. Select

All memory is cleared, and the calculator is reset to the factory settings.

When you reset the TIN73, the display contrast is reset. To adjust the contrast, follow the directions in the previous section.

2:Reset

The Home Screen

The Home screen is the primary screen of the TIN73. To go to the Home screen from any other screen or menu, press - l.

On the Home screen, you can enter instructions, functions, and expressions. The answers are displayed on the Home screen. The TIN73 screen can display a maximum of eight lines with a maximum of 16 characters per line.

When you calculate an entry on the Home screen, depending upon space, the answer is displayed either directly to the right of the entry or on the right side of the next line.

If an entry is longer than one line on the Home screen, it wraps to the beginning of the next line.

Chapter 1: Operating the TIN73

If all lines of the display are full, text scrolls off the top of the display. The TIN73 stores the previous entries as memory permits. See the section entitled, Retrieving Previous Entries on page 17.

You can scroll up with $ to see

If you

previously entered entries press b while a previous entry is highlighted (for example, 2+2+2+2+2+2+2+2), the calculator copies it to a new line below all entries (after 4+4+4 and its result, 52).

To clear the Home screen, see the section entitled Editing Numbers and Characters on page 11.

Entering Numbers and Other

Scroll up with $.

Characters

A symbol or abbreviation of each keys primary function is printed in white on the key. When you press that key, the function name is inserted at the cursor location.

Entering a Negative Number Entering a Negative Number a

You enter a negative number with the negation key, a. You can use negation to modify a number, expression, or each element in a list. Notice that this is different from the subtraction key, T, which CANNOT be used for negation.

Subtract M14 N 68.

-l:

14T68

Chapter 1: Operating the TIN73

Entering a Number in Scientific Notation Entering a Number in Scientific Notation -

Using - {, you can enter a number in scientific notation. The notation used to display the result of a calculation depends upon the

setting (

Normal

Sci

). For more information on selecting modes, see the section in this chapter entitled Mode Settings.

4 + 8600.

Add 30

-l:

-{\

8600

Entering Secondary Functions Entering Secondary Functions -

The - ke

The secondary function of each key is printed in yellow above the key. When you press the yellow - key, the yellow character, abbreviation, or word above a key, becomes active for the next keystroke.

, which is the same as pressing - and

TEXT

MATH

- t

then 1, displays the Text editor.

displays four math menus.

{

If in mode

If in

Normal

mode

Sci

Entering Text Entering Text

- t

Many examples in this manual require you to enter alphabetic characters, braces, a quotation mark, a space, or test operators. You can access all of these from the Text editor.

To exit the Text editor without saving the contents on the entry line, press - l, and the calculator returns you to the Home screen.

Chapter 1: Operating the TIN73

In all guidebook examples, when a character in the Text editor needs to be selected, the keystroke sequence shows the character followed by b. Moving the Selection Cursor as necessary to highlight the character is implied. To exit the Text editor and display the contents on the entry line on the

previous screen, select

Done

-t

The entry line

Selection CursorHighlights the character you want to

select. Use the cursor keys (", !, $, and #) to move the cursor.

is highlighted

with the selection cursor in the - t example screen.

Letters

(A-Z)

List Braces

{ }

Quotation Mark (

) Places a space between characters. It is

Space (

Test Operators

=, , >, , <, 

Logic (Boolean) Operators

and, or

Lists letters A-Z in alphabetical order.

Surround a set of numbers separated by commas to create a list (outside of the List

on the Home

editor). For example,

{1,2,3}

screen is interpreted as a list.

) Surrounds the first text element in a

categorical list or surrounds an attached list formula. (See Chapter 5: Lists for more information.)

frequently used in programs.

Used to compare two values.

Used to interpret values as zero (false) or nonzero (true).

Chapter 1: Operating the TIN73

Done

Exits the Text editor when selected and pastes all contents on the entry line to the cursor location on the previous screen.

Entry Line

Displays all currently selected characters.

ll edit keys, except the cursor keys, edit

characters on the entry line.

Insert R on the Home screen.

1. Go to the Home screen and

clear it, if desired.

-l:

2. Use the Text editor to

select

-t

3. Exit the Text editor.

Done

Use $, #, ", and

to highlight R.

is pasted to

the entry line.

The Home screen

Test and Logic (Boolean) Operators

You select test and logic operators exactly as you would a letter. Both types of operators are explained in detail in Chapter 2: Math Operations.

Chapter 1: Operating the TIN73

Entry Line

The entry line displays all characters selected in the Text editor. The entry line also accepts all number keys (Y, Z, [, ) and many keyboard operations (6, I, \, C, etc.). Enter these between Text editor characters, as necessary, without leaving the Text editor.

If you press a key that isnt accepted in the Text editor, the calculator does not return an error. You must select exit and then continue your entry on the previous screen.

You can enter up to 16 characters on the entry line. If you need

to save your

to enter more than 16 characters, select entry. Then reenter the Text editor, and continue entering additional characters.

Done

Common Display CursorsCommon Display Cursors

In most cases, the appearance of the cursor indicates what happens when you press the next key or select the next menu item.

If you press - while the Insert Cursor (Û) is displayed, the underline cursor becomes an underlined #.

Cursor Appearance Effect of Next Keystroke

Entry Solid RectangleÙA character is entered at the

cursor; any existing character is overwritten.

Insert Underline

Second Reverse ArrowÛA 2nd character (yellow on the

Full Checkerboard

Rectangle

A character is inserted in front of the cursor location.

keyboard) is entered, or a 2nd operation is executed.

No entry; the maximum characters are entered at a prompt, or memory is full.

Chapter 1: Operating the TIN73

Editing Numbers and CharactersEditing Numbers and Characters

Using the edit keys, you can edit an entry on the Home screen or Y= editor, programming commands in the Program editor, the entry lines of the Text editor and List editor, and constants in the Set Constant editor.

Keystrokes Result

! or " Moves the cursor to the left or right. Moves the

Selection cursor in the Text editor.

$ or # Moves/scrolls the cursor up or down.

- ! Moves the cursor to the beginning of an entry.

- " Moves the cursor to the end of an entry.

: • Within a line on the Home screen, it

clears all characters to the right of the cursor.

• At the beginning or end of a line on the

Home screen, it clears the current line.

• On a blank line on the Home screen, it

clears everything on the Home screen.

• In an editor, it clears the expression or

value where the cursor is located.

/ Deletes the character at the cursor.

- m Inserts characters in front of a character; to

end insertion, press - m or press !, ", $ or #.

< Inserts a character before a fraction on the

Home screen. (- m inserts a character before a fraction on any other screen.)

I Inserts the variable

at the cursor location.

Chapter 1: Operating the TIN73

Functions and Instructions

A function returns a value. Generally, the first letter of each function is lowercase on the TIN73. For example, function because it returns a value,

An instruction initiates an action. Generally, the first letter of each instruction name is uppercase. For example, instruction that draws a pixel on the graph screen.

Most functions and some instructions take at least one argument. An open parenthesis ( instruction name prompts you to enter an argument. Complete the function with an end parenthesis, E.

Note: Do not use the Text editor to enter names of functions or instructions. For example, you cannot enter

to calculate the log of a value. If you did this, the calculator

would interpret the entry as implied multiplication of the

, and G.

variables

When this guidebook describes the syntax of a function or instruction, each argument is in italics. Optional arguments for a function are signified by brackets [ ]. Do not enter the brackets.

L, O

or 1.

) at the end of the function or

(

pxl-Test(

Pxl-On(

, then O, then

is a

is an

Accessing Functions and Instructions from MenusAccessing Functions and Instructions from Menus

You can find most functions and instructions on menus (in other words, not directly from the keyboard).

Displaying a Menu

To display a menu, press the key associated with the menu. Up to four separate menus are displayed from which you choose the menu item you want.

Chapter 1: Operating the TIN73

To move from menu to menu on a menu screen, press " or ! until the menu name is highlighted.

When a menu item ends in an ellipsis (), the item displays a secondary menu or editor when you select it.

-‚

Accessing and Selecting Menu Items

To scroll up or down the menu items, press $ or #. To wrap to the last menu item directly from the first menu item, press $. To wrap to the first menu item directly from the last menu item, press #.

When the menu continues beyond the displayed items, a $ replaces the colon next to the last displayed item.

Select a menu item in one of two ways:

• Press # or $ to move the cursor to the number or letter

of the item, and then press b.

• Press the number key for the number next to the item. If

a letter is next to the item, access letters from the Text editor (- t).

After you select an item from a menu, you usually are returned to the initial screen where you were working.

Exiting a Menu without Making a Selection

Exit a menu without making a selection in one of three ways:

• Press : to return to the screen where you were.

• Press - l to return to the Home screen.

• Press a key or key sequence for another menu or for

another screen (except - t, which is not accessible from all screens).

Chapter 1: Operating the TIN73

Accessing FunctionsAccessing Functionsà

Instructions from theInstructions from the

CATALOGCATALOG

- | displays the

CATALOG

list of all functions, instructions, programming commands, variables, and symbols on the TIN73. If, for example, you cannot remember where a particular menu item is located, you can find it in the

CATALOG

Items that begin with a number are in alphabetical order according to the first letter after the number. For example,

1-Var Stats

is among the items that begin with V.

Items that are symbols follow the last item that begins with You can access the symbols quickly by pressing $ from the

. The cursor moves to the bottom of the

first catalog item,

A§b/c

list.

Selection Cursor

To select an item from the

CATALOG

, which is an alphabetical

1. Press - | to display the

CATALOG

. The Selection

Cursor always points to the first item.

2. Press $ or # to scroll the

CATALOG

until the Selection

Cursor points to the item you want.

To jump to the first item beginning with a particular letter, select that letter from the Text editor. Press - t while in the

CATALOG

, use the cursor keys to highlight the

letter you want, and then press b. You are automatically returned to the

CATALOG

, and the Selection Cursor has now moved to the new section. Scroll to the item you want.

3. Press b to paste the

CATALOG

item to the current

screen.

Chapter 1: Operating the TIN73

Enter the

1. Go to the

2. Select L from Text editor.

Selecting ¨ by pressing b pastes it to the previous screen, just as if you had selected it from a menu.

CATALOG

-t

and go directly to the section starting with

CATALOG.

Entering Expressions

An expression is a group of numbers, variables, functions and their arguments, or a combination of these elements that evaluates to a single answer. Instructions cannot be used in expressions. An expression is completed when you press b, regardless of the cursor location.

On the TIN73, you enter an expression in the same order as you would write it on paper. The entire expression is evaluated according to the Equation Operating System (EOS rules (which is explained in detail in Appendix B: Reference Information), and the answer is displayed.

Calculate the area (A) of a circle whose radius (R)=3 using the

formula A=pR of a cylinder whose height (H)=4. Use the formula V=AQH.

. Then use the area to calculate the volume (V)

-l: 6b

-„



)

Chapter 1: Operating the TIN73

M4b

is the previous

Ans

answer, 28.27433388.

Grouping Parts of Expressions with ParenthesesGrouping Parts of Expressions with Parentheses

The calculator calculates an expression within parentheses first.

Calculate 4(1+2).

-l:

4D1\2

4(1+2)=4(3)=12

Using Implied Multiplication in ExpressionsUsing Implied Multiplication in Expressions

The calculator understands that two numbers separated by parentheses are multiplied together.

Calculate 4Q3 using parentheses.

-l: Eb

4D3

Entering Multiple Expressions on One LineEntering Multiple Expressions on One Line

To store more than one expression on a line, separate two or more expressions or instructions on a line with a colon (- | $ $ $ b)

Define the variable, R=5, and then calculate pR2 on the same

line.

1. Store 5 to

-l:

X-t

Done

$$$b

Chapter 1: Operating the TIN73

2. Enter the second

, and

expression,

calculate the result.

-„-t b

Done

Retrieving Previous Entries -

When you press b on the Home screen to evaluate an expression or execute an instruction, the expression or

(last entry).

instruction is placed in a storage area called When you turn off the TIN73,

is retained in memory.

Entry

You can retrieve the last entry to the current cursor location, where you can edit it, if desired, and then execute it. On the Home screen or in an editor, press - £; the current line is cleared and the last entry is pasted to the line.

The TIN73 retains as many previous entries as memory permits. To cycle through these entries, press - £ repeatedly. To view stored entries, use $ to scroll up the Home screen.

Store 1 to variable A, 1 to variable B, and then 3 to variable A

using - £.

1. Store 1 to

-l:

X-t

Done

2. Recall the last entry.

-£

Chapter 1: Operating the TIN73

3. Edit and enter the new expression.

!-t

4. Cycle back two entries.

-£-£

5. Edit and enter the new expression.

!!!

Done

Recalling and Storing the Last Answer

When an expression is evaluated successfully from the Home screen or from a program, the TIN73 stores the answer to a

(last answer). Recall

system variable called pressing - ¢. turn off the TIN73, the value in

Ans

can be a real number or a list. When you

Ans

is retained in memory.

Ans

You can use the variable for the type of answer real number, you can use it anywhere where real numbers are accepted (Y= editor,

WINDOW

in any place that is appropriate

Ans

represents. For example, if

Ans

, List editor, etc.).

Continuing a Calculation with AnsContinuing a Calculation with Ans

You can recall without entering the value again or pressing - ¢. After completing a calculation, press an operation or function key (excluding <, =, or @) and the calculator displays and uses the value in the next calculation.

as the first entry in the next expression

Ans

is a

Ans

Chapter 1: Operating the TIN73

1. Calculate 34 using the

Ans

feature.

-l: b

3M3

2. Check your answer, if desired.

374

Using Ans as a Variable in an ExpressionUsing Ans as a Variable in an Expression

Since you would any other variable. When the expression is evaluated, the TIN73 uses the value of For more information about variables, see the next two sections in this chapter entitled, Storing Values to a Variable and Recalling Variable Values.

is a variable, you can use it in expressions just as

Ans

in the calculation.

Ans

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. Calculate the area.

-l:

1.7M4.2

2. Divide 147 by

, which

Ans

was calculated in the first step.

F-¢b

147

Ans=7.14

Chapter 1: Operating the TIN73

Storing Values to a Variable Storing Values to a Variable X

You can store values or expressions that result in one value or lists to a one-letter variable or a system variable (types are listed below) to save for later use. Also, you can save a result

to a variable before you evaluate

for later use by storing another expression.

When an expression containing the name of a variable is evaluated, the value of the variable at that time is used. You can enter and use several types of data for variables, including real numbers, lists, functions, statistical plots, and graph pictures.

Variable names cannot be the same as a name that is preassigned by the TIN73. These include built-in functions

, instructions such as

such as such as

abs( Xmin

Variable Type Names

Ans

, and system variables

Line(

)

, and any user-defined

}

)

2:Y-Vars

)

from the

Real Numbers

ListsNumerical and Categorical

Functions

Stat Plots

, , Z (-

A, B

list names (-

Y Plot1, Plot2, Plot3

Program editor)

Graph Pictures

System Variables

Pic1, Pic2, Pic3 Xmin, Xmax

,  (-

}

4:Picture

1:Window

Store a value to either a system variable or a letter variable from the Home screen or a program using the

key. Begin

on a blank line and follow these steps.

)

Chapter 1: Operating the TIN73

1. Enter the numeric value. It can be an expression that results in a numeric value.

2. Press X. " is copied to the cursor location.

3. Select the type of variable to which you want to store the value. Use the Text editor (- t) to enter a letter

(- }) menu to enter a system

variable, the variable, or the - v

VARS

menu to enter a list name.

4. Press b. If you entered an expression, it is evaluated. The value is stored to the variable.

Store 10 to R, and then calculate pR

1. On the Home screen, store

10 to

-l: X-t

Done

2. Calculate

-„-t

Done

Recalling Variable Values Recalling Variable Values

- P

To recall a variables value to the current cursor location, follow these steps. To leave

1. Press - P.

and the edit cursor are displayed on

Rcl

, press :.

Rcl

the bottom line of the screen.

2. Enter the name of the variable in any of four ways:

• Enter letters using the Text editor (- t).

• Press - v, and then select the name of the list

menu.

from the

Chapter 1: Operating the TIN73

• Press - } to display the

menu; next select

VARS

the type and then the name of the variable or function.

• Press 8 (from the Program editor only), and then

select the name of the program to call a program as a subroutine within another program.

3. The variable name you selected is displayed on the bottom line and the cursor disappears.

4. Press b. The variable contents are inserted where the cursor was located before you began these steps.

function. (R was defined in the

Calculate 100+R using the

Rcl

previous section, Storing Variable Values.)

1. On the Home screen, enter the first part of the calculation.

-l:

100

2. Recall R.

-P-t b

Done

3. Finish the calculation.

b b

Mode Settings

Mode settings control how the TIN73 interprets and displays numbers. Mode settings are retained by the Constant Memory feature when the TIN73 is turned off. All numbers, including elements of lists, are displayed according to the current mode settings, as applicable. To display the mode settings, press .. The default settings are highlighted on the following screen.

=10

Chapter 1: Operating the TIN73

To select a mode setting, highlight the one you want by using the cursor keys, and then press b.

Default

Settings

Normal Sci Float 0123456789 Degree Radian A§b/c b/c Autosimp Mansimp

Numeric Notation mode

Decimal Notation mode

ngle mode

Display Format mode (fractions only)

Simplification mode (fractions only)

Numeric Notation ModeNumeric Notation Mode

The Numeric Notation mode settings affect the way an answer is displayed on the TIN73. Numeric answers can be displayed with up to 10 digits and a two-digit exponent. Answers (excluding fractional ones) on the Home screen, list elements in the List editor, and table elements on the Table screen are displayed according to the Numeric Notation mode selected.

setting displays results with digits to the left and

Normal

The right of the decimal, as in

The

(scientific) setting expresses numbers with one digit to

Sci

123456.78

the left of the decimal and the appropriate power of 10 to the right of

, as in

1.2345678 © 5

, (which is the same as

Note: Answers that have more than 10 digits and whose absolute value is greater than .001 are displayed in scientific notation.

123456.78

Chapter 1: Operating the TIN73

Decimal Notation ModeDecimal Notation Mode

The Decimal Notation mode has two settings,

0123456789

on the TIN73.

The digits, plus the sign and decimal.

, which only affect the way an answer is displayed

(floating decimal point) setting displays up to 10

Float

and

0123456789

The number of digits (

(fixed decimal point) setting specifies the

through 9) to display to the right of the

decimal. Place the cursor on the desired number of decimal digits, and then press b.

The decimal setting applies to answers (excluding fractional ones) on the Home screen, X- and Y-coordinates on a graph display, list elements in the List editor, table elements on the Table screen, and regression model results.

Angle ModeAngle Mode

The Angle mode has two settings,

Degree

control how the TIN73 interprets angle values in trigonometric functions. See Chapter 11: Trigonometry for a detailed explanation.

and

Radian

, which

Display Format ModeDisplay Format Mode

The Display Format mode has two settings, which determine if a fraction is displayed as a mixed or simple fraction. See Chapter 3: Fractions for a detailed explanation.

A§b/c

and

Simplification ModeSimplification Mode

The Simplification mode has two settings,

Mansimp

, which determine if the calculator automatically

Autosimp

simplifies a fractional result completely or if you must simplify the results manually step-by-step. See Chapter 3: Fractions for detailed information.

and

b/c

Math OperationsMath Operations

Keyboard Math Operations ................................................27

Basic Operations \, T, M, F..................................... 27

Integer Division - Œ............................................28

p - „........................................................................ 28

Percent C....................................................................29

Inverse Function - ƒ .............................................30

Square 6 ....................................................................30

Power 7 ......................................................................31

Square Root - z .................................................... 31

Test Operations - t........................................... 32

The 1 MATH Menu ........................................................ 34

lcm( 1 1 ..................................................................35

gcd( 1 2..................................................................36

(Cube) 1 3 ...........................................................37

( 1 4 ....................................................................38

 1 5 .....................................................................38

Solver 1 6............................................................... 38

The 1 NUM Menu.......................................................... 44

abs( 1 " 1.............................................................. 44

round( 1 " 2 ......................................................... 45

iPart( and fPart( 1 " 3 and 4 ............................... 46

min( and max( 1 " 5 and 6..................................47

remainder( 1 " 7.................................................. 48

The 1 PRB Menu ............................................................49

rand 1 " " 1 ........................................................ 49

randInt( 1 " " 2 ..................................................50

nPr 1 " " 3 .......................................................... 51

nCr 1 " " 4 .......................................................... 51

! 1 " " 5 ..............................................................52

coin( 1 " " 6........................................................53

dice( 1 " " 7........................................................53

Chapter 2: Math Operations

The 1 LOG Menu ........................................................... 54

log( 1 " " " 1 .................................................... 54

10^( 1 " " " 2.................................................... 55

ln( 1 " " " 3 ...................................................... 55

e^( 1 " " " 4...................................................... 56

Chapter 2: Math Operations

Keyboard Math Operations

The following sections explain how to use the math functions, including - functions, found on the TIN73 keyboard. All of the examples in these sections assume that you are on the Home screen and that defaults are selected (unless specified otherwise).

Real numbers include fractions unless specified otherwise.

Basic Operations Basic Operations \

Returns the sum (\), difference (T), product (M), or quotient (F) of valueA and valueB, which can be real numbers, expressions, or lists.

If both values are lists, they must have the same number of elements. If one value is a list and the other is a non-list, the non-list is paired with each element of the list, and a list is returned.

valueA + valueB valueA N valueB valueA ¦ valueB valueA P valueB

Add M456 + 123.

:a b

Divide 45.68 P 123.

45.68F123

, , T

456\123

, , M

, , F

Multiply log(20) Q cos(60).

1"""

EM-u

Degree

mode

Chapter 2: Math Operations

Integer Division Integer Division -

- Œ

quotient and the remainder,

You can include integer division in an expression, but the remainder may not be displayed as part of the final answer.

After a calculation with quotient from the result is stored in Therefore, if you use the result in another calculation, the remainder is ignored.

Calculate 11 P 2 using integer

division.

divides two positive integers and displays the

posintegerA

posintegerB

Intà

quotient=5

remainder=1

-Œ

5r1

11 10

is completed, only the

(last answer).

Ans

The result includes the quotient and the remainder, r.

„

Represents the value for the constant, p, in calculations. The calculator uses p=3.1415926535898, although it only displays

3.141592654 on the screen. p acts as a real number in any calculation.

Multiply 4 Q p.

: „b

M-

Calculate sin(p).

:-u „E b

Chapter 2: Math Operations

If in mode

Radian

If in

Percent Percent

Changes a real_number to percent. Results display according to the Decimal Notation mode setting.

real_number%

Convert M30.6% to a decimal.

1. Select Float Decimal setting.

.#b

-l

2. Convert M30.6% to a decimal.

30.6

Calculate 20% of 30.

CM30b

Degree

mode

Calculate 30 + 20% of 30.

30\20

CM30b

Chapter 2: Math Operations

Inverse Function Inverse Function -

Returns the inverse, x-1, of value, which is the equivalent of the

reciprocal,

/x, of a real number, expression, or each element

in a list.

-1

value

Important: To ensure that results are displayed as simple fractions instead of mixed numbers, select

Display Format

b/c

mode.

-1

Calculate

5=8

"-ƒ

Calculate M2.5-1.

-ƒb

2.5

Square Square 6

Finds the square of a real number, an expression, or each element in a list. Note: Using parentheses with 6 ensures that you get the correct answer. Refer to Appendix B: Reference Information for Equation Operating System (EOS) calculation rules.

value

Calculate 52.

Compare the results of M52 and (M5)2..

1. Calculate M5

2. Calculate (M5)2..

E6b

Chapter 2: Math Operations

Power Power

Square Root Square Root

Raises value to any power. value and power can be real numbers, expression, or lists. If both are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non-list is paired with each element of the list, and a list is returned.

value^power

value is limited by mathematical rules. For example, (M4)^.5

results in an error because this is the equivalent of (M4)^ which is

Calculate 2

M4, a complex number.

275

- z

Calculates the square root of value, which can be a positive real number, an expression that results in a positive real number, or a list of positive numbers.

(value

)

/2,

Calculate 256.

:-z b

256

Chapter 2: Math Operations

Test Operations Test Operations -

The two types of test operations included in the Text editor are relational operators ( operators (

Both relational and logic operators often are used in programs to control program flow and in graphing to control the graph as a function over specific values.

and

and or).

, , >, , <, and ) and logic (Boolean)

Relational Operators

Relational operators compare conditionA and conditionB and return the conditional statement is false. conditionA and conditionB can be real numbers, expressions, or lists.

If both conditions are lists, they must have the same number of elements. If one condition is a list and the other a non-list, the non-list is compared with each element of the list, and a list is returned.

Test operations are frequently used in programs.

Relational operators are evaluated after mathematical functions according to EOS rules (Appendix B: Reference Information). Therefore, for 2+2=2+3, the TI-73 returns compares 4 with 5 and returns 0, because the operation is false. For 2+(2=2)+3, the TI-73 returns parentheses returns 1, because the operation is true. Then it adds 2+(1)+3.

if the conditional statement is true. They return 0 if

conditionA

relational_operator

conditionB

. The relational test in

. It

Chapter 2: Math Operations

Operator: Returns true (1) if:

(equal) Two conditions are equal.

(not equal to) Two conditions are not equal.



(greater than) conditionA is greater than conditionB.

(greater than or



equal to)

(less than) conditionA is less than conditionB.

(less than or



equal to)

conditionA is greater than or equal to conditionB.

conditionA is less than or equal to conditionB.

Logic (Boolean) Operators

Logic (Boolean) operators compare conditionA and conditionB and return

They return

if the conditional statement is false. conditionA

and conditionB can be real numbers, expressions, or lists.

if the conditional statement is true.

conditionB

conditionA conditionA

and

conditionB

Operator: Returns true (1) if:

Both conditions are nonzero.

t least one condition is nonzero.

and or

Test

/2 =16/32.

-l "

1=2

-t

Done

=true

b 16=32b

Chapter 2: Math Operations

For

L1={1,2,3}

1. Define

:-t

b1¡2¡

{

b X-v

2. Test

-v b

Test

cos(90) and sin(0)

:-u

-u

The 1

MATH

, test

> log(30)

Done

log(30)

-t

Done

1 30

E-t

Done

1 0

and

MATH Menu

menu includes various math functions.

1>log(30) 2>log(30) 3>log(30)

is false;

is true;

is true.

Chapter 2: Math Operations

1:lcm(

Finds the least common multiple, which is the smallest number that two integers can divide into evenly.

2:gcd(

Finds the greatest common divisor, which is the largest number that divides into two integers evenly.

(



5: 6:Solver…

lcm( lcm( 1

Calculates the cube.

Calculates the cube root.

Calculates the xth root.

Displays the Equation Solver.

1 1

The least common multiple (LCM) function returns the smallest number that two positive whole numbers can divide into evenly, of two positive whole numbers or lists of positive whole numbers. If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non-list is paired with each element of the list, and a list is returned.

is frequently used with fractions to find a common

lcm(

denominator. See Chapter 3: Fractions for more information on entering fractions.

valueA,valueB

lcm(

Find the LCM of 6 and 9.

¡9Eb

)

Chapter 2: Math Operations

Add 1/4 + 5/6 (using LCM).

1. Find the LCM of the denominators.

¡6Eb

2. Use the LCM to convert 1/ and 5/6to fractions where 12 is the common denominator (without using the calculator).

3. Add the newly converted fractions (without using the calculator).

4. Verify your answer by adding the original fractions on the calculator. Select the

Display Format mode

b/c

setting and clear the Home screen, if desired.

.###"b

-l: "\5=

1=4

Therefore, 12 is the common denominator.

3 3

2 2

10 12

LCM=12

13 12

5 6

gcd( gcd(

2 2

The greatest common divisor (GCD) function returns the largest number that divides into two positive whole numbers or lists of positive whole numbers evenly. If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non-list is paired with each element of the list, and a list is returned.

This is frequently used with fractions to reduce them to lowest terms. See Chapter 2: Fractions for more information on entering fractions.

valueA,valueB

gcd(

Chapter 2: Math Operations

)

Find the greatest common divisor for the fraction, 27/

1. Find the GCD of 27/36.

¡36Eb

GCD=9

2. Simplify the fraction

9 9

3 4

completely using the GCD (without using the

calculator).

3. Verify your answer by

simplifying

/36 by 9 on the

calculator. You must be in

Mansimp

mode setting.

.####" b-l

27=36

3 3

Calculates the cube of n, which is equivalent to n Q n Q n of any real number, expression, or each element in a list.

Calculate 53.

= 5 Q 5 Q 5 = 125

Chapter 2: Math Operations

( ( 1



4 4

Calculates the cube root of value, which is equivalent to n where n

=value. value can be a real number, expression, or

list.

For n3=value,



value

)

(

value=n

Calculate



(125).

5 5

4 125

Calculates the xth root of value, which is equivalent to n where

=value. value can be a real number, expression, or list. x

can be any real number.

For nx=value,



(

value

Calculate

64.

Solver Solver 1

)

6 6

value=n

The Equation Solver allows you to solve for one unknown one-letter variable in an equation containing up to 5 one-letter variables. By default, the equation is assumed to be equal to 0; however, you can set the equation equal to any real number (or an expression that results in a real number).



(125) = 5

because 5



64 = 2

because 2

=125

=64

depends on

The screen you see when you select

Solver

whether an equation has been defined previously.

To exit Solver and return to the Home screen, press -

Chapter 2: Math Operations

The EQUATION SOLVER Screen

If no equation is currently defined, pressing 1 6 takes you to the

EQUATION SOLVER

screen. Enter the equation at the

cursor, using the Text editor (- t) to enter the variable names.

You can have more than one variable on each side of the equation. For example,

A + B = B + D + E

If you do not set the equation equal to a value, the calculator automatically sets it equal to 0. For example, to enter A+B=0,

and press b. You are limited to 5 variables

just enter

A+B

per equation.

The Equation Variables Screen

If an equation has been defined previously, pressing 1 takes you to the Equation Variables screen.

Your screen

may vary.

Chapter 2: Math Operations

Equation Displays the currently defined

equation.

Equation Variables Displays all equation variables and

their values.

bound

Default={M1©99,1©99}

Displays the the unknown variable value for which

limits that apply to

bound

you are solving.

Solve

You select one variable, the one you want to solve for, from this list.

Equation

The first line of the Equation Variables screen displays the equation you defined on the

EQUATION SOLVER

screen.

If you would like to edit a defined equation, press $ until the

EQUATION SOLVER

screen is displayed. Edit the equation with

:, /, or - m, as necessary. Then press b to return to the Equation Variables screen.

Equation Variables

All variables included in the defined equation are displayed. If those variables have never been assigned a value, they are set equal to 0. If a variable has been defined previously (for example, from the Home screen), that value appears.

If a value extends beyond the screen, press " to scroll to the end of the number. This is especially important if a number is in scientific notation and you need to see whether it has a negative or positive exponent.

For an equation with more than one variable, you must define all variables except the unknown variable for which you want to solve.

Chapter 2: Math Operations

bound

limits apply to the unknown variable value for which

bound

you are solving. Default bounds are {M1©99,1©99}. Use these limits to narrow the unknown value solution to a specific range of numbers, especially if more than one answer exists.

Hint: For answers with many solutions (for example, trig functions), consider graphing the function first to get an idea

limits.

of the most ideal (or specific)

bound

Solve

Specify the unknown variable from the prompts the calculator to solve for it.

line, highlight the unknown

To select a variable on the

Solve

variable with the cursor, and then press b. After you press b, a solid black square appears next to the solved

(previously unknown) variable displayed in the Equation Variables section.

Hint: The Solver allows for a small tolerance when solving a result, which is noticeable especially when solving complex equations or those with multiple solutions. For example, a result of 3.99999999999999 (instead of 4) for the equation is considered a correct answer.

Solve

line. This

16=x

Solving Equations with Only One Possible Answer

For 2(L+M)=N, solve for L when N=268, and M=40, M14, and

307.

1. Define the equation on the

EQUATION SOLVER

$: (if necessary)

screen.

Chapter 2: Math Operations

2. Enter the equation.

-t

b\Mb

2DL

bNb

Done

3. Enter the first value for M, 40, and

, 268.

40#268

4. Solve for L.

##b

5. Solve for L when M=M14.

###b

6. Solve for L when M=307.

###b

307

Your variable values may vary.

Solving Equations with More Than One Answer

The calculator only returns one solution even if more than one possible solution exists. When this is the case, you can first enter a guess by assigning a value to that variable and then asking the calculator to solve your equation. The TI-73 always chooses the solution closest to that guess. However, the guess must be within the bound limits; otherwise, you get an error.

Chapter 2: Math Operations

Find the negative solution to the equation, 16=X2.

1. Define the equation on the

EQUATION SOLVER

screen.

$: (if necessary)

2. Enter the equation.

-t bI6

16=

Done

Your X value may vary.

3. Use

bound

to limit your

answer to a negative one (between M16 and 0).

#"a

//"

///

4. Solve for X.

5. The guess,

X=10

, is not between the limit bounds. You must clear or change it. (This step uses a different guess, M6.)

6. Solve for X.

##b

6 is between

the bounds.

Chapter 2: Math Operations

The 1

The 1 functions.

1:abs(

2:round( 3:iPart( 4:fPart( 5:min(

6:max(

7:remainder(

NUM

NUM Menu

(number) menu includes seven different math

Calculates the absolute value of a real number, list, or expression.

Rounds a real number, list, or expression.

Returns only the integer part of a result.

Returns only the fractional part of a result.

Returns the minimum of two real numbers, lists, or expressions.

Returns the maximum of two real numbers, lists, or expressions.

Returns the remainder resulting from the division of two real numbers or lists.

abs( abs( 1

Returns the absolute value of a real number, expression, or each element in a list. For an expression, the expression is calculated and the absolute value of that result is returned.

Find the absolute value of M35.2.

abs(

value

)

1" b

1 1

1a35.2

Chapter 2: Math Operations

round( round( 1

Returns a number, expression, or each element in a list rounded to 10 digits or #decimal_places (9), if specified. The final result is always displayed according to the Decimal Notation mode ( which overrides the current setting. Notice that the Decimal Notation mode settings do change the display but not the value of the result. Therefore, the entire result is stored in the calculator ready to use for future calculations, as applicable.

round(

Round p to different numbers of decimal places using different

Decimal Notation mode settings.

1. Set Decimal Notation mode

Float

2. Round p to 3 decimal

places.

2 2

) unless #decimal_places is specified,

value[,#decimal_places]

, if necessary.

.#b

-l:

1" ¡

-„

)

3. Set Decimal Notation mode .

.#""""" b-l

4. Round p to 3 decimal

places.

-£b

Chapter 2: Math Operations

5. Leave the Decimal Notation mode at

and round p to 5

digits.

-£!! b

iPart( and fPart( iPart( and fPart(

returns the integer part of a real number, expression, or

iPart(

1 "

3 and 4 3 and 4

each element in a list. For an expression, the expression is calculated and the integer part of the result is displayed.

value

iPart(

returns the fractional part of a real number, expression,

fPart(

)

or each element in a list. For an expression, the expression is calculated and the fractional part of the result is displayed.

If value is a mixed number, the fractional part is returned and displayed according to the current Simplification mode setting.

value

fPart(

Find the integer and fractional part of 23.45.

)

1. Set Decimal Notation mode

Float

.#b

-l

2. Find the integer part.

:1"

23.45

3. Find the fractional part.

23.45

Chapter 2: Math Operations

Find the fractional part of 1 1/

1=2

min( and max( min( and max(

4 1

"Eb

1 "

These are identical to the the - v

(minimum) returns the smaller of two values or the

min(

MATH

menu.

5 and 6 5 and 6

and

min(

commands found on

max(

smallest element in one list. value can be a real number, expression, or a list.

If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non-list is compared with each element of the list, and a list is returned.

valueA,valueB

min(

list

min(

(maximum) functions exactly like

max(

)

, but it always

min(

returns the larger of two values or the largest element in a list.

valueA,valueB

max( max(

list

)

For this example, the Decimal mode settings are set to

Compare

L2={3,2,1}

1. Define

and

to find the

in the List

min(

and

max(. L1={1,2,3}

and

editor.

For more information on entering lists, see Chapter 5: Lists.

Float

, and

Chapter 2: Math Operations

2. Find the list minimums.

-l: 1"

-v1¡

-v

3. Find the list maximums.

-v1¡

-v

remainder( remainder(

1 "

7 7

Returns the remainder resulting from the division of two positive whole numbers, dividend and divisor, each of which can be a list of positive whole numbers. They also are subject to mathematical rules. For example, divisor0.

remainder(

dividend,divisor

)

If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non-list is paired with each element of the list, and a list of remainders is returned.

remainder( remainder( remainder(

Calculate 10P6 and return

the remainder only.

list,divisor dividend,list list,list

)

divisor=6

10 8

dividend=10

remainder=4

:1"

¡6Eb

Chapter 2: Math Operations

The 1

The 1 that are often used to calculate probabilities.

1:rand 2:randInt( 3:nPr

4:nCr

5:! 6:coin( 7:dice(

PRB Menu

(probability) menu lets you select functions

PRB

1""

Generates a random number between 0 and 1.

Generates a random integer between two values.

Calculates the number of permutations for a group of items.

Calculates the number of combinations for a group of items.

Calculates the factorial of a positive integer.

Simulates one or more coin tosses.

Simulates one or more dice rolls.

rand rand 1

Generates a random real number between 0 and 1 (0<number<1).

rand

If you want to control a sequence of random numbers, first store an integer seed value to a specific sequence of random numbers from each seed value. To get a different sequence, use a different seed value. The default seed value is 0.

seed X

1 1

takes no arguments.

rand

. The calculator generates

rand

Chapter 2: Math Operations

Generate a sequence of random numbers using whatever value

happens to be the current seed.

:1""

bbb

Your results may vary.

Generate a sequence of random numbers using seed=1.

: "

X1"

b1""

randInt( randInt(

1 " "

2 2

Generates a random integer between lower and upper (both integers) boundaries.

The random integer returned may be one of the boundaries. For example,

randInt(1,5)

may return 1, 2, 3, 4, or 5.

To generate more than one random integer, specify

#ofIntegers, a positive whole number >0.

lower,upper[,#ofIntegers]

randInt(

)

Find a random integer from 2 through 10.

:1""

¡10Eb

Find 4 random integers from 2

through 10. (Recall and edit the last entry.)

-£!¡

Your result may vary.

Chapter 2: Math Operations

nPr nPr 1

3 3

Returns the number of permutations of n items taken r number at a time. The order in which you select the items DOES matter. items and number can be nonnegative integers or lists of nonnegative integers.

If both arguments are lists, they must have the same number of elements. If one argument is a list and the other a non-list, the non-list is paired with each element in the list, and a list of permutations is returned.

number

nPr

items

From a group of 4 items (ABCD), how many ways can you

select 2 of the items if the order does matter?

Find 4

ABCD

nPr

permutations of

4 items taken

1""

2 at a time

AB AC AD BA BC BD CA CB CD DA DB DC

AB and BA count as two permutations.

nCr nCr 1

4 4

Returns the number of combinations of n items taken r number at a time. In combinations, the order in which you select the items DOES NOT matter. items and number can be nonnegative integers or lists of nonnegative integers.

number

nCr

items

Chapter 2: Math Operations

From a group of 4 items (ABCD), how many ways can you

select 2 of the items if the order does not matter?

nCr

Find 4

1""

combinations of

4 items taken

2 at a time

5 5

AB AC AD

BC BD

CB CD

DB DC

AB and BA count as only one combination.

ABCD

! !

1 " "

Returns the factorial of value. value can be an integer or list of integers between 0 and 69. By definition, 0! = 1.

Factorials are similar to permutations because the order DOES matter. You can think of 4! as the total number of ways that 4 items can be arranged.

value

Find 4!

: b

1""

24 possible arrangements

4! = 4Q3Q2Q1

ABCD

ABCD ABDC ACBD ACDB ADBC ADCB BACD BADC BCAD BCDA BDCA BDAC CABD CADB CBAD CBDA CDAB CDBA DABC DACB DBAC DBCA DCAB DCBA

Chapter 2: Math Operations

coin( coin( 1

6 6

Returns a random list of 0s and 1s that represents heads and tails for one or more coin tosses. tosses is a positive whole number.

tosses

coin(

Simulate tossing a coin 7 times.

dice( dice( 1

)

:1""

7 7

4 heads and 3 tails (or 3 heads and 4 tails). Your result may vary.

Returns a random list of numbers (between 1 and 6) that represents dice rolls.

takes one optional argument,

dice(

#ofdice, a positive whole number>1. If #ofdice is specified, each list element is the total sum of one rolls results.

rolls[,#ofDice]

dice(

Simulate 5 dice rolls for one die.

:1""

Simulate 5 rolls of 3 dice.

)

Your result may vary.

:-£

!¡

The three dice totaled 11 on the first roll, 10 on the second roll, etc. Your result

vary.

Chapter 2: Math Operations

The 1

The 1 are used to calculate base-10 and base-e logarithms and powers.

1:log( 2:10^( 3:ln( 4:e^(

log( log( 1

The logarithm is the exponent, x, indicating the power which a fixed number (using base 10) must be raised to in order to produce a given number, a.

LOG Menu

(logarithm) menu lets you select functions that

LOG

1"""

NorN

Returns the base-10 logarithm of a value.

Raises 10 to a power.

Calculates the natural logarithm of a value.

Raises e to a power (e = 2.71828182846).

1 1

For 10x=a, log10a=x

returns the logarithm of a positive real number, an

log(

expression that results in a positive real number, or a list of positive real numbers.

value

log( log(

Calculate log(30).

)

list

)

:1"""

Chapter 2: Math Operations

10^( 10^( 1

Raises 10 to a power of x, where x is an integer, an expression that results in an integer, or a list of integers. If x10 the result is displayed in scientific notation.

10^( 10^(

Calculate 10^(6), which is often written as 106.

Calculate 10^(M4).

ln( ln( 1

The natural logarithm is the exponent, x, indicating the power which the base, e, must be raised to in order to produce a given number, a.

2 2

integer x

)

:1"""

1""" a4Eb

3 3

or 1010,

For ex=a, ln(a)=x

The calculator uses e=2.718281828459, although it only displays 2.718281828 on the screen.

returns the natural logarithm of a positive real number, an

ln(

expression that results in a positive real number, or a list of positive real numbers.

value

ln( ln(

list

)

Chapter 2: Math Operations

Calculate ln(1/2).

:1"""

=2"Eb

e^( e^(

1 " " "

Raises e to a power of x, where x is a real number, an expression that results in an real number, or a list of real numbers.

The calculator uses e=2.718281828459, although it only displays 2.718281828 on the screen.

e^(x)

list

)

e^(

Calculate e^5, which is often written as e5.

:1"""

4 4

FractionsFractions

Entering Fractions................................................................58

Using Fractions in Calculations ...........................................59

Fraction Modes ....................................................................60

Display Format Mode Settings ..................................... 60

Simplification Mode Settings ....................................... 60

Autosimp Setting .......................................................... 61

Mansimp Setting ........................................................... 62

Converting Between Fractions and Decimals ....................64

Converting Between Mixed Numbers

and Simple Fractions ..............................................65

Chapter 3: Fractions

Entering Fractions

Simple fractions consist of a numerator and denominator. Mixed numbers combine a whole number with a fraction. Note: The numerator and denominator cannot be a fraction.

Simple Fractions

numerator = denominator "

Enter

1. Enter the numerator, 2.

2. Enter the denominator, 3.

3. End the fraction.

/3.

Mixed Numbers

whole_number < numerator = denominator "

Enter 1

1. Enter the whole number, 1.

2. Enter the numerator, 2.

3. Enter the denominator, 3.

4. End the mixed number.

/3.

2 3

Continue the calculation at the cursor.

1 <

Chapter 3: Fractions

Using Fractions in Calculations

The type of calculation and the input values determine whether the results of a calculation are shown as a fraction or a decimal. You can enter fractions with all operation keys (\, M, F, etc.), most function keys (6, C, ƒ, etc.), and many menu items (

Fractional calculations return fractional results, if possible, except for those that:

abs(, fPart(, sin(

, etc.).

1000

MATH

TRIG

log(, ln(, e^(

and

ANGLE

CALC

;

• Use - „, C,  or 

• Calculate to a result

1000

or <



 or 

• Include both a fraction and a

decimal

 or 

• Use items from the following

menus: - ‚;

- v

- u

Chapter 3: Fractions

Fraction Modes

Two fraction modes exist on the calculator: Display Format mode and Simplification mode.

Display Format Mode SettingsDisplay Format Mode Settings

The Display Format mode settings, whether or not a fractional result is displayed as a mixed number or a simple fraction. To select a mode setting, press ., highlight the setting with the cursor keys, and then press b.

A§bàc

and

, determine

bàc

Displays result as a mixed number, if applicable.

Displays result as a simple fraction.

/5.

4=5

"\8=

A§b/c b/c

Add

Simplification Mode SettingsSimplification Mode Settings

The Simplification mode settings,

Autosimp

determine whether or not a fractional result is simplified automatically.

and

Mansimp

In mode

A§b/c

b/c

mode

Chapter 3: Fractions

Autosimp

The calculator automatically simplifies fractional results.

Mansimp

The user simplifies fractions manually step-bystep. $ next to the result signifies that it can be simplified at least one more time.

Add

1=9

"\5=

The total shaded area in the first diagram is equal to the total shaded area in the second one.

2 3

Autosimp SettingAutosimp Setting

In this example, Display Format mode settings do not affect the display of the result because the result is a simple fraction.

Autosimp

mode

Mansimp

mode

Add

1. Select

2. Add 1/

/4 + 1/4.

Autosimp

mode, if necessary, and return to the Home screen.

.####b

-l

/4.

"\1=4b

1=4

Chapter 3: Fractions

Mansimp SettingMansimp Setting

When the

Mansimp

calculation is not simplified automatically. means that it is unsimplified and can be simplified at least one more time. You then can decide if you want the calculator to simplify the result step-by-step using simplification factors it chooses or if you want the calculator to simplify the result using the simplification factors that you choose.

Letting the Calculator Choose the Simplification Factor

After getting an unsimplified result (one with $ next to it) from any fractional calculation, press B b. The simplified result and simplification factor which the calculator chose are displayed. For example, The Display Format mode settings affect whether a result is displayed as a mixed number or a simple fraction.

setting is selected, the result of a

next to a result

means simplification factor=3.

Fac=3

1. Select

Mansimp

mode setting, if necessary, and return to the Home screen.

.####" b-l

2. Add 1

+ 2

:1<3=4"\

<4=8b

3. Let the calculator simplify the result.

A§b/c

mode

b/c

mode

A§b/c

mode

b/c

mode

Chapter 3: Fractions

Choosing the Simplification Factor

After getting an unsimplified result from any fractional calculation, press B simplification_factor b, where simplification_factor is a positive integer that you choose. The Display Format mode settings affect whether a result is displayed as a mixed number or as a simple fraction.

Add

the sum to lowest terms.

1. Enter

2. Simplify by 2.

3. Simplify by 3.

/16 and choose the simplification factor to reduce

/16.

-l:

"\8=

4=16 16

The result did not change. Try again with another factor.

4. Simplify by 2.

Simplification is complete.

Recalling the Factor -

If you execute a fractional calculation in

}

6:Factor

Mansimp

mode and then the user or the calculator simplifies the result, you can recall the simplification factor at a later time by selecting

- }

Since

Factor

6:Factor

is a variable, you can use

in expressions or

Factor

on any screen that accepts whole numbers (Y= editor, List editor, Home screen, etc.).

Chapter 3: Fractions

Only one simplification factor (the last one calculated) is stored in memory. Also, you can store a positive whole

using the X key, just as you would store a

number to number to any variable. For more information about storing values to variables, see Chapter 1: Operating the TIN73.

From the Home screen, simplify 6/

recall the factor.

Factor

by a factor of 2, and then

mode, if

6=8

1. Select

2. Enter the fraction and

3. Recall the simplification

Mansimp

necessary.

.####" b-l

simplify.

: b

factor,

Converting Between Fractions and Decimals

To convert a fraction to a decimal or a decimal to a fraction, use >. If a fractional equivalent of a decimal does not exist, the calculator returns the same decimal number. Also, the calculator only recognizes and converts (if possible) the first ten digits of any decimal number.

You must follow > with b; otherwise, you get an error.

The current Decimal Notation mode determines the display of the result. In the following example, the calculator is set to

Decimal Notation mode.

Float

Chapter 3: Fractions

Convert 3/4 to a decimal and back to a fraction.

1. Convert

/4 to a decimal.

-l: >b

3=4

2. Convert .75 back to a fraction.

Add 2 plus the decimal equivalent of 1/4.

2\1=4

Converting Between Mixed Numbers and Simple Fractions

To convert a mixed number to a simple fraction or a simple fraction to a mixed number use ?. The Display Format mode settings do not affect the results when using ?.

You must follow ? with b; otherwise, you get an error.

Convert 3

1. Convert 3 fraction.

to a simple fraction and back to a mixed number.

to a simple

-l: <1=3?

Autosimp

mode

Mansimp

mode

/4=.25

2. Convert 10/3 back to a mixed number.

Chapter 3: Fractions

MeasurementMeasurement Conversions andConversions and

ConstantConstant CalculationsCalculations

The - ‚ CONVERSIONS Menu...............................68

Length - ‚ 1 .................................................68

Area - ‚ 2 ..................................................... 68

Volume - ‚ 3 ................................................69

Time - ‚ 4 .....................................................69

Temp (Temperature) - ‚ 5........................... 69

MassàWeight - ‚ 6....................................... 69

Speed - ‚ 7 ................................................... 69

Converting a Unit of Measure...................................... 70

Constants .............................................................................71

Single Mode ..................................................................72

Multiple Mode ..............................................................75

Chapter 4: ConversionsàConstants

The -

‚

CONVERSIONS Menu

Use this menu to access all conversion categories.

-‚

1:Length 2:Area 3:Volume 4:Time 5:Temp 6:MassàWeight 7:Speed

Length Length -

........... millimeters

............ centimeters

.............. meters

.......... inches

inch

Displays the

‚

LENGTH AREA VOLUME TIME TEMPERATURE MASS/WT. SPEED

1 1

ft yard km mile

menu.

.................... feet

................ yards

.................. kilometers

................ miles

menu.

Area Area -

............. square feet

............ square meters

............ square miles

.......... square kilometersha................... hectares

.......... acres

acre

‚

2 2

.................. square inches

................. square centimeters

................. square yards

Chapter 4: ConversionsàConstants

Volume Volume -

........... liters

liter

............ gallons

gal

.............. quarts

.............. pints

............. ounces

........... cubic centimeters

Time Time -

............ seconds

sec

........... minutes

min

.............. hours

‚

3 3

4 4

Temp (Temperature) Temp (Temperature) -

......... degrees Celsius

degC

......... degrees Fahrenheit

degF

......... degrees Kelvin

degK

MassMassà

Weight Weight -

............... grams

............. kilograms

.............. pounds

‚

...................cubic inches

...................cubic feet

...................cubic meters

.............UK gallons

galUK

..............UK ounces

ozUK

.................days

day

...............weeks

week

................years

year

‚

5 5

6 6

ton (US) mton (US)

..........tons

.......metric tons

Speed Speed -

........... feet per second

ftàs

.......... meters per second

màs

........ miles per hour

miàhr

‚

7 7

......... kilometers per hour

kmàhr

............ knots

knot

Chapter 4: ConversionsàConstants

Converting a Unit of MeasureConverting a Unit of Measure

To convert a measurement value, enter the measurement value, select the category from the

CONVERSIONS

the unit you are converting from, and then the unit you are converting to. To know which category to select, look at the units of the original value. You can only convert within one category.

measurement_value current_unit 4 new_unit

Convert 50 meters to inches.

1. Clear the Home screen, if desired. Enter the value, 50.

-l:

menu, select

2. Display the

CONVERSIONS

menu.

-‚

3. Select the applicable category,

1:LENGTH

4. Select the current unit, meters.

5. Select the unit which you want to convert to, inches.

6. Calculate the result.

The current unit is displayed.

m8 inch

to the Home screen.

is pasted

Chapter 4: ConversionsàConstants

EOS operating rules (Appendix B: Reference Information) apply when converting negative measurements as shown in the next example.

¡F4¡

Compare the results of M5

C and (M5)¡F4¡C.

1. From the Home screen,

¡F4¡

calculate M5

-l:

-‚

The calculator converts 5¡F to ¡C

and then returns the negative of the result.

2. Calculate (M5)¡F4¡C..

-£-!

-mD""

-mEb

The calculator converts (M5)¡F to ¡C.

Constants

To save time re-entering long or complicated expressions and to help prevent entry errors, you can enter numbers, expressions, lists, commands, or functions into the calculators memory by defining them as constants in the Set Constant editor. As constants, they then can be recalled at any time.

You can define up to four constants in the Set Constant editor

and choose from one of two different modes: The mode you select determines how many of the constants you can recall at a time. To enter a constant in the editor, select the mode from the Set Constant editor (- †), move the cursor to one of the four constants, and define it.

Single

Multiple

-†

Chapter 4: ConversionsàConstants

To use a constant:

1. Define the constant in the Set Constant editor (- †).

2. Recall the constant with the @ key.

Single ModeSingle Mode

By selecting want to access one constant from the list, even if more than one is defined.

To select the one constant ( highlight the automatically deselects any other defined constants.

Defining Constants in Single Mode

Enter the constants in the Set Constant editor as shown in the following example. At any time you can enter this editor and edit, delete, or add constants.

mode, you tell the calculator that you only

Single

, or

next to it, and then press b. This

) you want to use,

Define

= +1/2 and

= ¦1/2.

1. Enter the Set Constant editor.

-†

2. Highlight

Single

with the

cursor, if necessary.

3. Define

as +1/2.

1=2

Chapter 4: ConversionsàConstants

4. Define

as ¦1/2.

## M

1=2

5. Exit the Set Constant editor.

-l

The most recently entered constant ( selected.

) remains

Single Mode Constant Calculations

After a constant is defined and selected, return to the screen where you want to use it in a calculation. Pressing @

mode, only one

=+ 1/

Single

pastes it to the cursor location. In defined constant is available for use in calculations, and an expression using a constant is automatically solved after pressing @ (without pressing b).

You recognize that

Calculate 40+

1. Select

Single

/2.

mode, if

necessary.

-†$b

2. Select

(which deselects

), and exit the Set

Constant editor.

#!b-l

3. Clear the Home screen, if desired. Solve the problem using

Count=1.

Recalling a Constant in a Series of Calculations

When pressing @ more than once in a series of calculations, the calculator automatically keeps count for you (shown in the following example) unless the defined constant includes a list. The counter starts over any time a new entry

precedes @, including

Ans

Chapter 4: ConversionsàConstants

Find the multiple of 2 so that 5 ¦ 2n=40.

The calculator’s constant counter automatically computes n.

Constant mode = Single Set

1. Select

5¦2n=40

mode, if

Single

necessary.

-†$b

2. Enter

##M

C2 = ¦ 2

3. Return to the Home screen and clear, if desired.

-l:

4. Count the number of times you have to multiply 5 by 2

to get 40 (so that 5 Q 2

=40).

Cn = ¦ 2

Other defined constants are deselected automatically.

5 Q 2 is calculated automatically.

Count=1

Solution

5¦2¦2¦2=40, or

5¦2

=40

n=3

Pressing @ a second time acts like - ¢ @.

n=3 because you multiplied by 2 three times in a row.

Chapter 4: ConversionsàConstants

Multiple ModeMultiple Mode

Multiple

any time. To define cursor keys, and then press b.

Defining Constants in Multiple Mode

You define constants in you define them in selected, even if they are not defined.

Select

previous examples.

1. Enter the Set Constant

mode, all defined constants are available to use at

Multiple

Single

mode and use the constants defined in the

Multiple

mode, highlight

Multiple

mode. All constants are always

editor.

-†

using the

Multiple

mode exactly the same way

2. Select

Multiple

mode.

$"b

All constants are now selected.

Recalling Constants in Multiple Mode

When you press @ from the Home screen and the Set Constant editor is in

Multiple

every defined constant is displayed. Undefined constants are

marked as

Empty

mode, the first six characters of

Chapter 4: ConversionsàConstants

To select a constant, press the number associated with the constant ( the same one) by pressing @ again. In (unlike in

, or 4). You may choose another constant (or

1, 2, 3

Multiple

mode), your constant expression is not

Single

evaluated until you press b.

mode

Define

C3=+3¦2

and

C4=¦2+3

-†$"b ###:

3M2

\ M

2\3

You recognize that

Calculate 4+3¦2.

1. Go to the Home screen and clear it, if desired.

-l:

2. Find the result.

@3b

You recognize that

Calculate 4¦2+3.

@4b

Multiple

=+3¦2

=¦2+3

mode.

Press b to evaluate the expression.

ListsLists

Steps for Creating a List ......................................................78

The List Editor 3 ............................................................ 79

Naming a List .......................................................................79

Entering List Elements......................................................... 81

Editing Lists in the List Editor .............................................87

Inserting or Deleting a New List ..................................87

Deleting Lists from Calculator Memory....................... 88

Inserting or Deleting One Element in a List ................89

Editing an Existing Element .........................................89

Clearing All Elements in a List......................................90

Clearing All Elements in All Lists.................................. 90

Editing a List Formula ................................................... 90

The - v Ls Menu ......................................................... 91

The - v OPS Menu......................................................92

SortA( and SortD( - v " 1 and 2 ......................93

ClrList - v " 3 ....................................................95

dim( - v " 4....................................................... 95

@List( - v " 5 .....................................................97

Select( - v " 6 ...................................................98

seq( - v " 7........................................................99

augment( - v " 8............................................ 100

¨ (List Signifier) - v " 9.................................101

List Commands from the Home Screen ............................ 102

Creating a List .............................................................102

Copying One List to Another .....................................103

Displaying One List Element....................................... 103

Inserting or Changing a List Element ........................104

Using Math Functions with Lists ................................105

Chapter 5: Lists

Steps for Creating a List

On the TIN73, a set of numerical or text information is called a list. Follow these basic steps when defining a list.

Display the List editor.

Name the list you want to define, or

use a prenamed list (

Enter list elements (numerical or text).

Edit list as necessary.

- t

(to name a list)

number keys

- t

Surround text elements

Note:

- m, :, or /

Prenamed lists,

, and one user-named

list,

PET

with quotation marks.

and

Chapter 5: Lists

The List Editor 3

You can enter up to 20 lists in the List editor. Each list can have up to 999 elements. You can only display three lists at the same time; use " or ! to scroll to see all other defined lists.

List notation looks like this:

L5={1,2,3,4,5,6}.

1, 2, 3, 4, 5, and 6 are stored in the list named

Entries in each column display the

first 6 characters of the element.

Entry line

, and one empty, unnamed list initially are

Read it as elements

.

List name across top

List counter (cursor is in the 1st list).

included in the List editor.

Numeric Notation, Decimal Notation, and Angle modes affect the display of an element (except fractional elements).

Fractions are unaffected by Numeric Notation mode.

Calculator is in

Numeric

Sci

Notation mode.

Highlighted element

Naming a List

is displayed on entry line in its entirety.

When you are ready to define your list, you can move to one of

the columns labeled

and begin entering your list

elements.

Chapter 5: Lists

If you do not want to use

(you cannot rename them), you

can create a new list and name it anything you want. A list name can be one to five characters long. The first character must be a letter from A to Z. The second through fifth characters can be any combination of letters and numbers. Access letters from the Text editor (- t ). A list accepts elements only after it is named.

Note: You cannot rename a user-named list, but you can copy its elements to a list with a different name. See the section entitled, Copying One List to Another on page 103.

In this guidebook, when a list name is referred to, its name is

always preceded by the

when naming a list in the List editor.

symbol; however, you dont type the

If a defined list name is highlighted, the list elements or the attached formula are displayed on the entry line.

Create a list named

1. Display the List editor.

NUM

Or, insert a blank list. Highlight a list name and press - m.

2. Scroll to the blank, unnamed list to the far right of the List editor.

" or !

3. Use the Text editor to name the list

NUM.

-t bUb

N M

4. Move 

NUM

Done

 from the entry

line to the list name line.

appears on

NUM

the entry line.

now

NUM

accepts elements.

Chapter 5: Lists

Entering List Elements

A named list accepts two types of elements: numerical and text.

• Lists that contain numerical elements not enclosed in

quotation marks are called numerical lists.

• Lists that contain text elements or numerical elements

whose numerical values are ignored (because they are enclosed in quotation marks) are called categorical lists.

To enter an element, highlight the space in the column under the list name where you want the element to be entered (you cant skip any spaces) and type in the element (it is displayed on the entry line). Press b or # to move the element into the list. Pressing # or b also moves the cursor to the next element space.

Access the quotation marks (for categorical lists) from the Text editor (- t ).

Numerical Lists

Numerical lists contain real numbers, fractions, or expressions that evaluate to real numbers or fractions. If you enter an

, the calculator displays the decimal

expression like equivalent in the list element space. The Numeric Notation, Decimal Notation, and Angle modes determine how the calculator displays all elements, except fractions.

sin(30)

Define

1. Go to the first element

NUM={18,25,45}

space of the numerical list

NUM

3 " (as necessary) # (if necessary)

Chapter 5: Lists

2. Enter the list elements.

18#25#45

Entering Fractional Elements

When entering fractions from the Home screen, parentheses are optional around the numerator and denominator.

When entering fractions in the List editor (and any other editor), parentheses are mandatory around the numerator and denominator ONLY when operators are included:

1\2=3\4

3 b

Interpreted as 1+(2/3)+4

D1\2E=

3\4

Using parentheses

Chapter 5: Lists

Dependent Numerical Lists

," and

¨NUM

) is

The numerical list described in the previous section ( an independent list. You also can create dependent lists, which are dependent (or based) upon the contents of another defined numerical list.

You create a dependent list by attaching a formula to it. For example,

"2 + L

," where

is already defined, is a formula. The

formula always contains at least one other list. In addition, for

a formula like

L3="2+L1+ L

and

number of elements. Then, each element in

must have the same

is the result of

the attached formula.

When a formula is attached to a list, a small signifier (2) appears next to the list name. You cannot edit a dependent list by simply typing over an element as with independent lists. You must highlight the element you want to change, press b, and then edit it. However, this changes the entire list back to an independent list, and the formula and the formula signifier disappear.

Also, it is possible to have multiple dependent lists all based on the same list (for example,

L4="4+L1"

L2="2+ L

L3="3+L

An attached formula can be enclosed in quotation marks (located in the Text editor). A list whose formula:

• Is not enclosed in quotation marks is not automatically

updated if the independent list changes.

• Is enclosed in quotation marks is automatically updated if

the independent list changes.

Convert the following six Celsius temperatures

{M40,M15,M5,30,58,140} to Fahrenheit and display both lists in the List editor.

Independent List

Dependent List

¨CEL={M40,M15,M5,30,58,140} ¨FRHT="¨CEL degC8degF"

Chapter 5: Lists

1. Create the independent list,

¨CEL

3 " or " (as necessary

to move to the blank list)

-t

b bLb bb

2. Enter the elements.

#a15#a

#30#58#

3. Create the dependent list,

¨FRHT

"-t

b RbHb

Done

140

4. Attach the formula

degC8degF"

"¨ CEL

¨FRHT

b-t

-v

-‚

Done

CEL

5 1 2

-t " b

Done

5. Display the elements of

¨FRHT

A small formula signifier appears.

Chapter 5: Lists

6. Change M5 in

!##ba

¨CEL

to M8.

: Since the formula is enclosed

Note

in quotation marks, element 3 in

is automatically updated.

FRHT

Categorical Lists

Categorical lists usually contain words or letters (text elements). If they contain numerical elements, the numerical values of those elements are ignored. Categorical lists are usually used in statistical plotting, but they can allow you to label elements as explained in the following example. See Chapter 6: Statistical Plots for details about using categorical lists in stat plots.

To define a categorical list, enclose the first element in quotation marks (found in the Text editor). Quotation marks are optional on the remaining text elements. A categorical list

, appears next to the list name.

signifier,

A math class has 4 test scores: 2 tests, 1 midterm test, and 1

final exam. Ivan earned test scores of 85, 80, 74, and 82. Karen earned test scores of 90, 85, 92, and 79. Reflect this information in the List editor.

1 Categorical

2 Numerical

¨TEST={TEST1,TEST2,MDTRM,FINAL} ¨IVAN={85,80,74,82} ¨KAREN={90,85,92,79}

Chapter 5: Lists

1. Display the List editor and create a list named

3"or ! (as necessary to move to the blank list)

-t bEb

bTb

Done

TEST

2. Enter the element

TEST1.

#-t " b

bEb

bTb

Done

3. Repeat for the elements

TEST2, MDTRM

, and

FINAL

(quotation marks are optional after the first element).

4. Create a list named

IVAN.

"-t

bVb

bNb

Done

5. Enter 85,

85#80#74

80, 74,

and 82.

The categorical list signifier, c.

Chapter 5: Lists

6. Create a list named

KAREN.

"-t

bAb

bEb

Done

7. Enter 90,

90#85#92

85, 92

, and 79.

Once you have these lists entered, you can display this data in various ways using related features on the calculator. For example, Chapter 6: Statistical Plots explains how you could easily convert this data into a bar chart. Chapter 7: Statistical Analyses explains ways to find each students averages as well as doing other statistical analyses of their test scores.

Editing Lists in the List Editor

From the List editor, you can display, edit, insert, temporarily delete (not from memory), and move from view all lists stored in the calculator. You also can edit, insert, move, or delete list elements and attached formulas.

To see all list names that are stored into the calculators memory (but not necessarily the List editor), display the

menu and use $ and # to scroll the menu.

- v

Inserting or Deleting a New ListInserting or Deleting a New List

Inserting a list into the List editor saves it in the calculators memory. However, deleting a list from the List editor does not delete it from the calculators memory. A deleted lists name

menu.

still appears in the - v

Therefore, if you would like to insert the deleted list back into the List editor, go to a blank list, select the list name from

menu and press b b.

- v

Chapter 5: Lists

Insert

between

and

1. Move the cursor so that it .

highlights

3$ "or ! (as necessary)

2. Insert a blank list.

-m

3. Identify it as

Delete

-v

Deleting Lists from Calculator MemoryDeleting Lists from Calculator Memory

To delete a list from the calculators memory, use the

- Ÿ

4:Delete

calculators memory, the names still appear in the - v menu. If you delete a user-named list, its name is deleted from this menu.

menu. If you delete



from the

If elements exist in L1, then those appear also.

Chapter 5: Lists

Delete memory.

from the calculators

-Ÿ

-l(to return to

the Home screen)

4 3

Inserting or Deleting One Element in a ListInserting or Deleting One Element in a List

To insert one element in a list:

1. Use the cursor keys as necessary to highlight the element space where you want to insert the element.

2. Press - m to insert the element space. All following elements move down one space.

3. Type the element, and press b.

To delete one element from a list:

1. Use the cursor keys as necessary to highlight the element that you want to delete.

2. Press / to delete the element. All following elements move up one space.

Editing an Existing ElementEditing an Existing Element

You can edit any particular element in a list without having to reenter the entire list.

1. Use the cursor keys as necessary to highlight the element that you want to edit.

2. Press b to move the element to the entry line.

3. Edit the element with - m, :, or /, as necessary.

4. Press b to replace the existing element with the edited element.

Chapter 5: Lists

Clearing All Elements in a ListClearing All Elements in a List

To clear all of the elements in a list when the List editor is displayed:

1. Use the cursor keys as necessary to highlight the list name. The list elements (or formula) are displayed on the entry line.

2. Press : b to clear the list elements.

You also can clear elements from the Home screen using the

- v

OPS 3:ClrList

menu item.

Clearing All Elements in All ListsClearing All Elements in All Lists

You clear all elements in all lists using the - Ÿ instruction from the Home screen. When you press b, all elements in all lists are cleared from the calculators memory, even for those lists not displayed in the List editor.

-l b

-Ÿ

6:ClrAllLists

Editing a List FormulaEditing a List Formula

To edit an attached formula:

1. Use the cursor keys as necessary to highlight the name of the list name that you want to edit.

2. Press b to move the formula to the entry line.

3. Edit the formula with - m, :, or /, as necessary.

4. Press b to replace the existing formula with the edited formula. The list elements are updated automatically according to the new formula.

Chapter 5: Lists

Deleting a List Formula

You can delete an attached formula in one of two ways. You can:

• Follow the preceding directions for editing a formula, but

press : b in place of step 3.

• Edit one of the elements in the dependent list as directed

in the steps for editing an element. When you are finished, the formula signifier disappears, and the list becomes independent.

The -

Ls Menu

Use the - v Ls (lists) menu to access all list names

stored in the calculators memory.

are listed first

followed by all user-named lists in alphabetical order. In this menu, the user-named lists appear as they do in the List editor

(the List signifier,

, does not precede the name). However, if

you select a list to display it anywhere else on the calculator,

such as the on Home screen, the

automatically appears

before the name.

-v

User-named lists follow

in alphabetical order.

From the Home screen, you can type in a new list name

directly using the Text editor (except for must precede the list name with the list signifier,

the list signifier, can access

- v

OPS

If you try to use the reads that

, is smaller than the L in the Text editor. You

by itself from - | or under the

menu.

from the Text editor, the calculator

plus any following characters as variables

); however, you

Notice that

(representing numerical values), not as a list.

Chapter 5: Lists

The -

Use the - v from the Home screen.

1:SortA(

(Ascending)

2:SortD(

(Descending)

3:ClrList 4:dim(

5:@List(

-v

OPS Menu

(options) menu to change defined lists

OPS

Sorts list elements from lowest to highest in numerical order or in alphabetical order.

Sorts list elements from highest to lowest in numerical order or in reverse alphabetical order.

Clears all elements in specified list(s).

Recalls, sets, or changes the dimension (number of elements) in a list.

Returns the differences between consecutive elements in a list.

6:Select(

7:seq(

8:augment(

Selects one or more specific data points from a Scatter or xyLine stat plot, and then updates the list(s) in memory. (Requires you to set up a statistical plot. See Chapter 6: Statistical Plots for more information.)

Returns a list that fulfills the requirements of 5 arguments (expression, variable, begin, end, and increment) which you specify.

Combines two lists to make a new list.

List signifier; all text characters or numbers following it are interpreted as a list name.

Chapter 5: Lists

SortA( and SortD( SortA( and SortD( -

(sort ascending) sorts numerical list elements from

SortA(

1 and 2 1 and 2

lowest to highest value and categorical list elements

(sort descending) sorts the list elements

alphabetically.

SortD(

from highest to lowest value or in reverse alphabetical order.

Enter the

SortA(

instruction on the Home screen; and

SortD(

then enter all list names that you want to sort (separated by a comma), and press

Sorting One List

list

SortA( SortD(

Define

order.

1. Define

2. From the Home screen, sort in ascending order.

)

list

)

L2={4,7,3,9}

in the List editor, and sort in ascending

in the List editor.

-l:

-v"

-v2E b

3. If desired, display

Home screen or in the List editor to see the new order.

-v

 or 

3 "

(as necessary)

on the

On the Home screen

In the List editor

Chapter 5: Lists

Sorting Multiple Lists

You can specify more than one list when using

. In this case, the first list specified is the independent

SortD(

one; any following lists are dependent.

The calculator sorts the independent list first, and then sorts all the dependent lists by placing their elements in the same order as their corresponding elements in the independent list. This allows you to keep sets of related data in the same order when you sort lists.

indpntlist,dependlist1,dependlist2

SortA(

indpntlist,dependlist1,dependlist2

SortD(

SortA(

) )

and

Define

L4={14,13,12,11}

L2={3,4,7,9}

(dependent), and sort all three in descending

order.

and

1. Define

L2, L3,

List editor.

2. From the Home screen, sort the lists in descending order.

-l:

-v"

-v2¡

-v

3. If desired, display the elements in the List editor to see the new order.

3 " (as necessary)

(independent),

in the

L3={1,2,3,4}

(dependent), and

{9} still corresponds

to L3{4} and L4{11} and so on.

Texas Instruments TI-73, TI-73 EXPLORER User Manual 2

Specifications and Main Features

Frequently Asked Questions

User Manual

Table of ContentsTable of Contents

Chapter 2: Math Operations 25

Chapter 3: Fractions 57

Chapter 4: Measurement Conversions and Constant Calculations 67

Chapter 5: Lists 77

Chapter 6: Statistical Plots 107

Chapter 7: Statistical Analyses 127

Chapter 8: Tables 149

Chapter 9: Function Graphing 163

Chapter 10: Drawing 187

Chapter 11: Trigonometry 209

Chapter 12: Programming 221

Chapter 14: Memory Management 275

Appendix B: Reference Information 319

Index 345

Installing the AAA BatteriesInstalling the AAA Batteries

Adjusting the Display ContrastAdjusting the Display Contrast

Resetting Memory and All DefaultsResetting Memory and All Defaults

The Home Screen

Entering a Number in Scientific Notation Entering a Number in Scientific Notation -

Entering Secondary Functions Entering Secondary Functions -

Entering Text Entering Text

Common Display CursorsCommon Display Cursors

Editing Numbers and CharactersEditing Numbers and Characters

Functions and Instructions

Accessing Functions and Instructions from MenusAccessing Functions and Instructions from Menus

Accessing FunctionsAccessing Functionsà

Entering Expressions

Grouping Parts of Expressions with ParenthesesGrouping Parts of Expressions with Parentheses

Using Implied Multiplication in ExpressionsUsing Implied Multiplication in Expressions

Entering Multiple Expressions on One LineEntering Multiple Expressions on One Line

Recalling and Storing the Last Answer

Continuing a Calculation with AnsContinuing a Calculation with Ans

Using Ans as a Variable in an ExpressionUsing Ans as a Variable in an Expression

Storing Values to a Variable Storing Values to a Variable X

Recalling Variable Values Recalling Variable Values

Mode Settings

Numeric Notation mode

Decimal Notation ModeDecimal Notation Mode

Angle ModeAngle Mode

Display Format ModeDisplay Format Mode

Simplification ModeSimplification Mode

Keyboard Math Operations

Basic Operations Basic Operations \

Integer Division Integer Division -

Percent Percent

Inverse Function Inverse Function -

Square Square 6

Power Power

Square Root Square Root

Test Operations Test Operations -

lcm(

gcd( gcd(

Solver

abs(

round(

iPart( and fPart( iPart( and fPart(

min( and max( min( and max(

remainder(

rand

randInt(

coin(

dice(

log(

10^( 10^( 1

Entering Fractions

Using Fractions in Calculations

Fraction Modes

Display Format Mode SettingsDisplay Format Mode Settings

Simplification Mode SettingsSimplification Mode Settings

Autosimp SettingAutosimp Setting

Mansimp SettingMansimp Setting

Converting Between Fractions and Decimals

Converting Between Mixed Numbers and Simple Fractions

Length Length -

Area Area -