Master Math: Pre-Calculus and Geometry

By Debra Ross

Copyright © 1996 by Debra Anne Ross

All rights reserved under the Pan-American and International Copyright Conventions. This book may not be reproduced, in whole or in part, in any form or by any means electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system now known or hereafter invented, without written permission from the publisher, The Career Press.

MASTER MATH: PRE-CALCULUS AND GEOMETRYISBN 1-56414-218-3 Cover design by The Visual Group Printed in the U.S.A. by Book-mart Press

Library of Congress Cataloging-in-Publication Data

Ross, Debra Anne, 1958- Master math: pre-calculus and geometry / by Debra Anne Ross.p. cm. Includes index. ISBN 1-56414-218-3 (pbk.) 1. Geometry. 2. Trigonometry. I. Title. QA445.R585 1996 515'.1--dc20 96-22994 CIP

Acknowledgments

I am indebted to Dr. Melanie McNeil, Professor of Chemical Engineering at San Jose State University, for reviewing this text for accuracy.

Table of Contents

Introduction

1

Chapter 1 Geometry

3

1.1. Lines and Angles

4

1.2. Polygons

10

1.3. Triangles

13

1.4. Quadrilaterals (Four Sided Polygons)

18

1.5. Circles

22

1.6. Perimeter and Area of Planar Two-Dimensional Shapes

29

1.7. Volume and Surface Area of Three-Dimensional Objects

34

1.8. Vectors

40

Chapter 2 Trigonometry

43

2.1. Introduction

43

2.2. General Trigonometric Functions

44

2.3. Addition, Subtraction and Multiplication of Two Angles

52

2.4. Oblique Triangles

53

2.5. Graphs of Cosine, Sine, Tangent, Secant, Cosecant and Cotangent

54

2.6. Relationship Between Trigonometric and Exponential Functions

58

2.7. Hyperbolic Functions

60

Chapter 3 Sets and Functions

62

3.1. Sets

62

3.2. Functions

65

Chapter 4 Sequences, Progressions and Series

70

4.1. Sequences

70

4.2. Arithmetic Progressions

71

4.3. Geometric Progressions

73

4.4. Series

74

4.5. Infinite Series: Convergence and Divergence

77

4.6. Tests for Convergence of Infinite Series

80

4.7. The Power Series

86

4.8. Expanding Functions into Series

88

4.9. The Binomial Expansion

92

Chapter 5 Limits

94

5.1. Introduction to Limits

94

5.2. Limits and Continuity

98

Chapter 6 Introduction to the Derivative

104

6.1. Definition

105

6.2. Evaluating Derivatives

110

6.3. Differentiating Multivariable Functions

113

6.4. Differentiating Polynomials

114

6.5. Derivatives and Graphs of Functions

114

6.6. Adding and Subtracting Derivatives of Functions

118

6.7. Multiple or Repeated Derivatives of a Function

119

6.8. Derivatives of Products and powers of Functions

120

6.9. Derivatives of quotients of Functions

125

6.10. The Chain Rule for Differentiating Complicated Functions

128

6.11. Differentiation of Implicit vs. Explicit Functions

131

6.12. Using Derivatives to Determine the Shape of the Graph of a Function (Minimum and Maximum Points)

134

6.13. Other rules of Differentiation

142

6.14. An Application of Differentiation: Curvilinear Motion

143

Chapter 7 Introduction to the Integral

146

7.1. Definition of the Antiderivative or Indefinite Integral

147

7.2. Properties of the Antiderivative or Indefinite Integral

150

7.3. Examples of Common Indefinite Integrals

152

7.4. Definition and Evaluation of the Definite Integral

153

7.5. The Integral and the Area under the Curve in Graphs of Functions

156

7.6. Integrals and Volume

160

7.7. Even functions, Odd Functions and Symmetry

162

7.8. Properties of the Definite Integral

164

7.9. Methods for Evaluating Complex Integrals; Integration by Parts, Substitution and Tables

165