# Introduction to Algebra and Trigonometry

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Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry. This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are likewise treated. Other topics include analytic geometry, conic sections, and use of a coordinate system to prove theorems from plane, and matrix operations and inverses. This publication is valuable to students aiming to gain more knowledge of the fundamentals of mathematics.

## Table of Contents

Preface

Acknowledgments

To the Student

Chapter One The Foundations Of Algebra

1.1 The Real Number System

1.2 The Real Number Line

1.3 Algebraic Expressions; Polynomials

1.4 Factoring

1.5 Rational Expressions

1.6 Integer Exponents

1.7 Rational Exponents and Radicals

1.8 Complex Numbers

Chapter Review Material

Chapter Two Equations And Inequalities

2.1 Linear Equations in One Unknown

2.2 Applications

2.3 Linear Inequalities

2.4 Absolute Value in Equations and Inequalities

2.5 The Quadratic Equation

2.6 Applications—Quadratic Equations

2.7 Second-Degree Inequalities

Chapter Review Material

Chapter Three Functions

3.1 Rectangular Coordinate Systems

3.2 Functions and Function Notation

3.3 Graphs of Functions

3.4 Linear Functions

3.5 Direct and Inverse Variation

3.6 Combining Functions; Inverse Functions

Chapter Review Material

Chapter Four Exponential And Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Properties of Logarithms

4.4 Computing with Logarithms (Optional)

4.5 Exponential and Logarithmic Equations

Chapter Review Material

Chapter Five Trigonometry: The Circular Functions

5.1 The Wrapping Function

5.2 The Sine, Cosine, and Tangent Functions

5.3 Graphs of Sine, Cosine, and Tangent

5.4 Variation of Sine, Cosine, and Tangent

5.5 Graphs: Amplitude, Variation, and Phase Shift

5.6 Secant, Cosecant, and Cotangent

5.7 The Inverse Trigonometric Functions

Chapter Review Material

Chapter Six Angles And Triangles

6.1 Angles and Their Measurement

6.2 Trigonometric Functions of Angles

6.3 Right Angle Trigonometry

6.4 Law of Cosines

6.5 Law of Sines

Chapter Review Material

Chapter Seven Analytic Trigonometry

7.1 Trigonometric Identities

7.2 The Addition Formulas

7.3 Double and Half-Angle Formulas

7.4 The Product-Sum Formulas

7.5 Trigonometric Equations

7.6 Trigonometry and Complex Numbers

Chapter Review Material

Chapter Eight Analytic Geometry: The Conic Sections

8.1 Analytic Geometry

8.2 The Circle

8.3 The Parabola

8.4 The Ellipse and Hyperbola

8.5 Identifying the Conic Sections

Chapter Review Material

Chapter Nine Systems Of Equations And Inequalities

9.1 Systems of Linear Equations

9.2 Solving by Elimination

9.3 Applications

9.4 Systems of Linear Equations in Three Unknowns

9.5 Systems Involving Nonlinear Equations

9.6 Systems of Linear Inequalities in Two Variables

Chapter Review Material

Chapter Ten Matrices And Determinants

10.1 Matrices and Linear Systems

10.2 Matrix Operations and Applications (Optional)

10.3 Inverses of Matrices (Optional)

10.4 Determinants and Cramer's Rule

Chapter Review Material

Chapter Eleven Roots Of Polynomials

11.1 Polynomial Division and Synthetic Division

11.2 The Remainder and Factor Theorems

11.3 Factors and Roots

11.4 Real and Rational Roots

11.5 Rational Functions and Their Graphs

Chapter Review Material

Chapter Twelve Topics In Algebra

12.1 Arithmetic Progressions

12.2 Geometric Progressions

12.3 Mathematical Induction

12.4 The Binomial Theorem

12.5 Counting: Permutations and Combinations

12.6 Probability

Chapter Review Material

Appendix/Tables

Answers To Odd-Numbered Exercises, Review Exercises, And Progress Tests

Index

## Product details

- No. of pages: 620
- Language: English
- Copyright: © Academic Press 1981
- Published: January 1, 1981
- Imprint: Academic Press
- eBook ISBN: 9781483263915

## About the Authors

### Bernard Kolman

#### Affiliations and Expertise

Drexel University

### Arnold Shapiro

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