Trigonometry Demystified - A Self-Teaching Guide

321 Pages·2003·5.4 MB·English

by  Stan Gibilisco

TRIGONOMETRY DEMYSTIFIED
[10:54 6/6/03 n:4070 GIBILISCO.751/4070-Prelims.3d] Ref: 4070 GIBILISCO Trigonometry Demystified Prelims Page: 1 1-14
This page intentionally left blank.
TRIGONOMETRY DEMYSTIFIED
STAN GIBILISCO
McGRAW-HILL
New York Chicago San Francisco Lisbon London
Madrid Mexico City Milan New Delhi San Juan
Seoul Singapore Sydney Toronto
[ 1 0 : 5 4 6 / 6 / 70 n:4070 GIBI-
ebook_copyright 7.5x9.qxd 9/29/03 11:40 AM Page 1
Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as per-
mitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any
means, or stored in a database or retrieval system, without the prior written permission of the publisher.
0-07-143388-0
The material in this eBook also appears in the print version of this title: 0-07-141631-5.
All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked
name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the
trademark. Where such designations appear in this book, they have been printed with initial caps.
McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate train-
ing programs. For more information, please contact George Hoare, Special Sales, at
To Tim, Tony, and Samuel
from Uncle Stan
[10:54 6/6/03 n:4070 GIBILISCO.751/4070-Prelims.3d] Ref: 4070 GIBILISCO Trigonometry Demystified Prelims Page: 5 1-14
This page intentionally left blank.
For more information about this title, click here.
CONTENTS
Preface xi
Acknowledgmentsxiii
PART ONE: WHAT IS TRIGONOMETRY?
CHAPTER 1 The Circle Model 3
The Cartesian Plane 3
Circles in the Plane 8
Primary Circular Functions 11
Secondary Circular Functions 15
Quiz 18
CHAPTER 2 A Flurry of Facts21
The Right Triangle Model 21
Pythagorean Extras 26
Identities 28
Quiz 34
CHAPTER 3 Graphsand Inverses 38
Graphs of Circular Functions 38
Inverses of Circular Functions 44
Graphs of Circular Inverses 50
Quiz 54
vii
Copyright © 2003 by The McGraw-Hill Companies, Inc. Click here for Terms of Use.
[10:54 6/6/03 n:4070 GIBILISCO.751/4070-Prelims.3d] Ref: 4070 GIBILISCO Trigonometry Demystified Prelims Page: 7 1-14
viii CONTENTS
CHAPTER 4 Hyperbolic Functions57
The Hyper Six57
Hyperbolic Inverses 64
Hyper Facts 69
Quiz 75
CHAPTER 5 Polar Coordinates78
The Mathematician’s Way 78
Some Examples 80
Compression and Conversion 89
The Navigator’s Way 92
Quiz 97
CHAPTER 6 Three-Space and Vectors100
Spatial Coordinates 100
Vectors in the Cartesian Plane 108
Vectors in the Polar Plane 111
Vectors in 3D 115
Quiz 121
Test: Part One 124
PART TWO: HOW IS TRIGONOMETRY USED?
CHAPTER 7 Scientific Notation 139
Subscripts and Superscripts 139
Power-of-10 Notation 141
Rules for Use 147
Approximation, Error, and Precedence 152
Significant Figures 157
Quiz 162
CHAPTER 8 Surveying, Navigation, and Astronomy 164
Terrestrial Distance Measurement 164
[10:54 6/6/03 n:4070 GIBILISCO.751/4070-Prelims.3d] Ref: 4070 GIBILISCO Trigonometry Demystified Prelims Page: 8 1-14
CONTENTS ix
Interstellar Distance Measurement 169
Direction Finding and Radiolocation 173
Quiz 182
CHAPTER 9 Wavesand Phase 185
Alternating Current 185
Phase Angle 189
Inductive Reactance 195
Capacitive Reactance 197
Quiz 201
CHAPTER 10 Reflection and Refraction 204
Reflection 204
Refraction 208
Snell’s Law 210
Dispersion 215
Quiz 220
CHAPTER 11 Global Trigonometry 224
The Global Grid 224
Arcs and Triangles 231
Global Navigation 243
Quiz 247
Test: Part Two 251
Final Exam 266
Answers to Quiz, Test, and Exam
Questions 293
Suggested Additional References 297
Index 298
[10:54 6/6/03 n:4070 GIBILISCO.751/4070-Prelims.3d] Ref: 4070 GIBILISCO Trigonometry Demystified Prelims Page: 9 1-14