Title TI-83 Graphing Calculator Manual - Cengage English 2.2 MB 105
```                            Title Page
Preface
Chapter 1 - The Six Trigonometric Functions
Chapter 2 - Right Triangle Trigonometry
Chapter 4 - Graphing and Inverse Functions
Chapter 5 - Identities and Formulas
Chapter 6 - Equations
Chapter 7 - Triangles
Chapter 8 - Complex Numbers and Polar Coordinates
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##### Document Text Contents
Page 2

Preface

Technology, used appropriately, enhances the teaching and learning of
mathematics. The purpose of this manual is to provide sequences of keystrokes
for developing calculator skills, to assist students in interpreting calculator
screens, and to relate the capabilities of technology with students’ analytical
skills. The ultimate goal is to deepen the students’ understanding of
trigonometry and its application to problem solving.

How to use this Manual.

Anytime you are asked to complete a command that is in capital letters, then you
are being asked to press a specific calculator key. For example if the directions
say ENTER then you should press the ENTER button on your calculator;
however, if the directions ask you to enter 4, then you are being asked to enter
the number 4--press the 4 key. After you are given a sequence of keys to press,
you will be given a calculator screen to compare with the screen of your
calculator.

ALERT will be used when caution needs to be exercised when using the
calculator. For example,

1

2x
, cannot be entered in the calculator as 1/2x.; the

calculator would interpret this as

1
2

x . Hence you would be alerted that you must

use parentheses and enter this as 1/(2x). The word Note will precede additional
information or the interpretation of a calculator screen.

Explanation of Exercises from the Text

Actual problems from the text are worked in this manual. Each section will be
identified and the specific problem number will be in bold print. Every time a
problem from the text is discussed, the necessary calculator skills are explained
as well as the necessary analytical skills. After completing the problem the
student is encouraged to interpret and to check the answe

Page 52

Chapter 4 TI-83

Can you see that the graph on the right is only half of the graph on the left?
You would have to extend the maximum x-value to 4π to see a complete period. The
length of the period for y = cos (x) is 2π and the length of the period for
y = cos ( 12 x) is 4π. ( 122π ÷ ) Compare these examples with the definition of period in

For any function y = ƒ(x), the smallest positive number p for which ƒ(x + p) = ƒ(x) for all
x is called the period of ƒ(x).

If B is a positive number, the graphs of Y = A sin (Bx) and y = A cos (Bx) will each have

a period of

B

.

Question 1 asks you to graph one complete cycle of y = sin (2x). Before you start to
enter this in your calculator, look at the function analytically and answer the following
questions. What is the period of y = sin (2x)? The coefficient of x is two--the B value

is two. You also know that the period is

B

. The period of y = sin (2x) is
2
2
π

or π .

The amplitude is 1. Now enter 2y sin x= this in your calculator and verify your
analytical calculations. Check your calculator screens with the screens that follow.

Note. As you sketch a graph on your paper, be sure to label all of the x and y-
intercepts.

Question 9 asks you to graph one complete cycle of y = csc 3x( ) .

csc

3x( ) =

1
sin 3x( )

Rodgers, K. 48

Page 53

Chapter 4 TI-83

Since the cosecant is the reciprocal of the sine function, you know that whenever the
sine function is equal to zero, the cosecant function is undefined. The sine function is
equal to zero at kπ where k is an integer. You also know that the period of the
cosecant function is equal to the period of the sine function; the cosecant function
does not have amplitude.

Before you start to graph y = csc 3x( ) , determine the period.

period =

3

(Remember that

B

gives the period.)

When 3x equals kπ (k is an integer), the cosecant function will be undefined. In other
words when x

=

k π
3

k is an integer( ), there will be a vertical asymptote. Now enter

press MODE
press ENTER
press Y=
enter

1

sin 3x( )

press WINDOW
enter 0 for Xmin

enter
2

for 3
π

Xmax

enter

π
3

for There is no best value for this x-scale; Xscl
π
3

was

chosen since the vertical asymptotes will occur at
multiples of

π
3

.

enter -5 for Ymin Select y-values for the minimum and the
maximum that permits you to see the shape of the
graph.

enter 5 for Ymax
enter 1 for Yscl
press GRAPH

49

Page 104

Chapter 8 TI-83

Rodgers, K.

100

enter ,
enter 2
press ENTER

The r-value returned is 4, the same as the r-value in the original problem. Now check
the angle value.

press 2nd and ENTER

Repeat theses keystrokes until your calculator recalls
2 cos 15( ) +i sin 15( )( )

2( )

press ENTER Since you want to use the ANS feature of the calculator,
you must have that expression entered preceding the
time it is to be used. When you use ANS the calculator
always recall the last answer that it gave.

press ANGLE
select R˛ Pθ( Returns θgiven x and y.
press MATH
select CPX
select real(
press ANS
enter )
enter ,
enter 2
press ENTER

The angle measurement returned is 30°, the same angle-value as in the original
problem.

Note. This is just one of several ways you could use your calculator to check this
problem.

Page 105

TI-83

APPENDIX A

:Disp “FORMULA”
:Disp “ AX2 + BX +C = 0”
:Disp: “A”
:Input A
:Disp “B”
:Input B
:Disp “C”
:Input C
:

oto 1

B2 − 4AC( ) →D( )
:If D < 0
:G
:

−B+ D( )( )/ 2A( ) →P( )

:

−B− D( )( )/ 2A( ) →Q( )

:Disp “REAL ROOTS”
:Disp “ROOT 1”
:Disp P
:Disp “ROOT 2”
:Disp Q
:Goto 2
:Lbl 1
:Disp “COMPLEX ROOTS”
: −B / 2A( )( )→W
:

ABS D( )( )/ 2A( ) →