Sharp EL-9600 Manual de usuario
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.
Copyright © 1998 by Sharp Electronics Corporation.
All rights reserved. This publication may not be reproduced,
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
π
2
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
π
3
π
3
×
+–
÷
▼
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