Sharp EL-9600 Manuale utente

APPLYING

USING THE

EL-9600

DAVID P. LAWRENCE

TRIGONOMETRY

SHARP

Graphing Calculator

SHARP TRIG COVER 02.2.19 10:55 AM Page 3

TRIGONOMETRY USING THE SHARP EL-9600 i

Applying

TRIGONOMETRY

using the

SHARP EL-9600

GRAPHING CALCULATOR

David P. Lawrence

Southwestern Oklahoma State University

This Teaching Resource has been developed specifically for use with the

Sharp EL-9600 graphing calculator. The goal for preparing this book was

to provide mathematics educators with quality teaching materials that

utilize the unique features of the Sharp graphing calculator.

This book, along with the Sharp graphing calculator, offers you and your

students 10 classroom-tested, topic-specific lessons that build skills.

Each lesson includes Introducing the Topic, Calculator Operations, Method

of Teaching, explanations for Using Blackline Masters, For Discussion,

and Additional Problems to solve. Conveniently located in the back of

the book are 36 reproducible Blackline Masters. You’ll find them ideal

for creating handouts, overhead transparencies, or to use as student

activity worksheets for extra practice. Solutions to the Activities are

also included.

We hope you enjoy using this resource book and the Sharp El-9600

graphing calculator in your classroom.

Other books are also available:

Applying STATISTICS using the SHARP EL-9600 Graphing Calculator

Applying PRE-ALGEBRA and ALGEBRA using the SHARP EL-9600 Graphing Calculator

Applying PRE-CALCULUS and CALCULUS using the SHARP EL-9600 Graphing Calculator

Graphing Calculators: Quick & Easy! The SHARP EL-9600

ii TRIGONOMETRY USING THE SHARP EL-9600

Dedicated to my grandma, Marjorie Lee

Special thanks to Ms. Marina Ramirez and Ms. Melanie Drozdowski for

their comments and suggestions.

Developed and prepared by Pencil Point Studio.

stored in a retrieval system, or transmitted in any form or by

any means, electronic, mechanical, photocopying, recording,

or otherwise without written permission.

The blackline masters in this publication are designed to be used with

appropriate duplicating equipment to reproduce for classroom use.

First printed in the United States of America in 1998.

TRIGONOMETRY USING THE SHARP EL-9600 iii

CONTENTS

CHAPTER TOPIC PAGE

1 Graphs of Trigonometric Functions 1

2 Evaluating Trigonometric Functions 5

3 Graphical Verification of

Formulas and Identities 10

4 Amplitude, Period and Phase Shift 14

5 Inverse Trigonometric Functions 19

6 Solving Trigonometric Equations 23

7 Applications with Right Triangles 29

8 Law of Sines and Law of Cosines 34

9 Area of a Triangle 41

10 Area of a Circular Sector 47

Blackline Masters 52

Solutions to the Activities 89

Graphs of Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600 1

GRAPHS OF

TRIGONOMETRIC FUNCTIONS

Chapter one

Introducing the Topic

In this chapter, you and your students will learn how to graph trigonometric

functions on the Sharp EL-9600. Graphing trigonometric functions on the

calculator is covered first, so that graphical evaluation of trigonometric

functions may be covered in the next chapter. The trigonometric functions

are often introduced as circular functions with angle measurement in degrees

and radians. The sine and cosine functions are said to map the angle

measurement to the yand xcoordinates respectively, of the point on the unit

circle representing the angle. Then, the four additional trigonometric functions

are defined in terms of sine and cosine.

If you let the angle measurement be represented by a horizontal axis (x) and let

the vertical axis (y) represent the function evaluated at the angle, then you can

graph the six trigonometric functions as y= sin x, y= cos x, y= tan x, y= csc x,

y= sec x, and y= cot x.

Calculator Operations

Turn the calculator on and press Y= . The Y prompts will appear in the viewing

window. Press CL to remove an old Y1 expression. Press ▼CL to clear

additional expressions. The calculator should be setup in radian measurement,

with rectangular coordinates, and in equation editor mode. To complete this

setup, press 2ndF SET UP , touch B DRG, double touch 2 Rad, touch

E COORD, double touch 1 Rect, touch G EDITOR, and double touch 1 Equation.

Press 2ndF QUIT again to exit the menu and return to the Y prompts.

To enter the sine function ( y= sin x) for Y1, press sin X/θ/T/n.

Enter the viewing window range by pressing ZOOM , touching E TRIG, and

double touching 1 sin x. This establishes built-in viewing-window range for

graphing the sine function. The window ranges are -2π≤x≤2πand -1.55 ≤y

≤1.55. The scale for the xaxis is and the y-axis scale is .5.

The remaining five trigonometric functions can be graphed similarly.

2Graphs of Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600

Method of Teaching

Use the Blackline Master 1.1 to create an overhead for graphing the sine

function. Go over in detail how to graph a trigonometric function. Follow

the sine function demonstration with the cosecant function demonstration

provided in the sample problem below and on the Blackline Master.

Next, use the Blackline Masters 1.2 through 1.4 to create worksheets for the

students. Have the students graph the remaining four trigonometric functions.

Use the topics For Discussion to supplement the worksheets. Engage the trace

feature by pressing TRACE . Move the tracer by pressing or . Tracing

will assist you in discussing the topics.

Using Blackline Master 1.1

The problem discussed above in the Calculator Operations section is presented

on Blackline Master 1.1. The following problem also appears on the

Blackline Master.

Graph the cosecant function by pressing Y= CL to remove an old Y1

expression. To enter the cosecant function for Y1, press MATH , you may

need to touch A CALC if the menu is not already there. Double touch 10 csc,

and press X/θ/T/n. Use the sine function's built-in viewing range, and press

GRAPH to view the graph.

Graphs of Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600 3

▼

For Discussion

You and your students can use the calculator to discuss:

(1) intervals where the functions increase and decrease,

(2) domain and range of the functions,

(3) the periodicity of the functions, and

(4) which part of the horizontal axis represents each quadrant.

The trace feature will allow you to move along the curve to see where the

function is increasing and decreasing, to see the values associated with limits

on the domain and range, to see the period of a function, and to explore the

quadrant "markers" on the x-axis.

4Graphs of Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600

Introducing the Topic

In this chapter, you and your students will learn how to evaluate trigonometric

functions directly in radians or degrees, and graphically through the tracing feature.

Calculator Operations

To evaluate sin 45° directly, you will turn the calculator on and press to

enter computation mode. Press CL to clear the viewing window of any old

expressions. To evaluate trigonometric functions in degrees, you can set the

calculator to operate in degrees by pressing 2ndF SET UP , touch B DRG,

and double touch 1 Deg. Press 2ndF QUIT to exit the menu. Now, to find the

sin 45° you will press sin 4 5 ENTER .

Evaluating Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600 5

EVALUATING TRIGONOMETRIC

FUNCTIONS

Chapter two

+–

To approximate sin 45° graphically, you will press Y= followed by CL to clear

an old expression for Y1. Enter the function sin xby pressing sin X/θ/T/n.

To view the graph press ZOOM , touch E TRIG, and double touch 1 sin x.

Now, engage the trace by pressing TRACE and moving the tracer near

x= 45° by pressing .

With the cursor located near x= 45°, you can zoom in to find a better

approximate for the yvalue. First, set the factors for zooming by pressing

ZOOM , touching B FACTOR, and pressing ENTER 5 ENTER 5 ENTER .

These larger values will accelerate the zooming in. Now, press ZOOM , touch

A ZOOM, and double touch 3 In to zoom in on the cursor. Once again, trace

over near x= 45°. Zoom in two more times to see a better approximation.

To find sin directly, you will turn the calculator on and press to enter

computation mode. Press CL to clear the viewing window of any old

expressions. To evaluate trigonometric functions in radian mode, you can set

the calculator to operate in radians by pressing 2ndF SET UP , touching

B DRG, and double touching 2 Rad. Press 2ndF QUIT to exit the menu.

Now, to find sin you will press sin 2ndF πa/b 3 ENTER .

6Evaluating Trigonometric Functions/TRIGONOMETRY USING THE SHARP EL-9600

+–

▼

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