# College Algebra and Trigonometry

**by**Ratti, J. S.; McWaters, Marcus S.

### 9780321644718

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## Summary

## Author Biography

**J.S.Ratti **has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the "Center for Mathematical Services" at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and known as the coauthor of a successful finite mathematics textbook.

**Marcus McWaters **is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eleven years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.

## Table of Contents

P. Basic Concepts of Algebra

P.1. The Real Numbers and Their Properties

P.2. Integer Exponents and Scientific Notation

P.3. Polynomials

P.4. Factoring Polynomials

P.5. Rational Expressions

P.6. Rational Exponents and Radicals

P.7. Topics in Geometry

Chapter P. Summary

Chapter P. Review Exercises

Chapter P. Practice Test

1. Equations and Inequalities

1.1. Linear Equations in One Variable

1.2. Applications of Linear Equations

1.3. Complex Numbers

1.4. Quadratic Equations

1.5. Solving Other Types of Equations

1.6. Linear Inequalities

1.7. Equations and Inequalities Involving Absolute Value

Chapter 1. Summary

Chapter 1. Review Exercises

Chapter 1. Practice Test A

Chapter 1. Practice Test B

2. Graphs and Functions

2.1. The Coordinate Plane

2.2. Graphs of Equations

2.3. Lines

2.4. Relations and Functions

2.5. Properties of Functions

2.6. A Library of Functions

2.7. Transformations of Functions

2.8. Combining Functions; Composite Functions

2.9. Inverse Functions

Chapter 2. Summary

Chapter 2. Review Exercises

Chapter 2. Practice Test A

Chapter 2. Practice Test B

Cumulative Review Chapters. P-2

3. Polynomial and Rational Functions

3.1. Quadratic Functions

3.2. Polynomial Functions

3.3. Dividing Polynomials

3.4. The Real Zeros of a Polynomial Function

3.5. The Complex Zeros of a Polynomial Function

3.6. Rational Functions

3.7. Polynomial and Rational Inequalities

3.8. Variation

Chapter 3 Summary

Chapter 3 Review Exercises

Chapter 3 Practice Test A

Chapter 3 Practice Test B

Cumulative Review Chapters P-3

4. Exponential and Logarithmic Functions

4.1. Exponential Functions

4.2. The Natural Exponential Function

4.3. Logarithmic Functions

4.4. Rules of Logarithms

4.5. Exponential and Logarithmic Equations

Chapter 4 Summary

Chapter 4 Review Exercises

Chapter 4 Practice Test A

Chapter 4 Practice Test B

Cumulative Review Chapters P-4

5. Trigonometric Functions Angles and Their Measure

5.1 Right Triangle Trigonometry

5.2 Trigonometric Functions of Any Angle; Unit Circle

5.3 Graphs of the Sine and Cosine Functions

5.4 Graphs of the Other Trigonometric Functions

5.5 Inverse Trigonometric Functions

Chapter 5 Summary

Chapter 5 Review Exercises

Chapter 5 Practice Test A

Chapter 5 Chapter Test B

Cumulative Review Chapters P-5

6. Trigonometric Identities

6.1 Verifying Identities

6.2 Sum and Difference Identities

6.3 Double-Angle and Half-Angle Identities

6.4 Product-to-Sum and Sum-to-Product Identities

6.5 Trigonometric Equations I

6.6 Trigonometric Equations II

Chapter 6 Summary

Chapter 6 Review Exercises

Chapter 6 Practice Test A

Chapter 6 Practice Test B

Cumulative Review Chapters P-6

7. Applications of Trigonometric Functions

7.1 The Law of Sines

7.2 The Law of Sines: Ambiguous Case

7.3 The Law of Cosines

7.4 Area of a Triangle

7.5 Vectors

7.6 The Dot Product

7.7 Polar Coordinates

7.8 Polar Form of Complex Numbers; DeMoivre’s Theorem

Chapter 7 Summary

Chapter 7 Review Exercises

Chapter 7 Practice Test A

Chapter 7 Practice Test B

Cumulative Review Chapters P-7

8. Systems of Equations and Inequalities

8.1 Systems of Linear Equations in Two Variables

8.2 Systems of Linear Equations in Three Variables

8.3 Systems of Nonlinear Equations

8.4 Systems of Inequalities

8.5 Linear Programming

8.6 Partial-Fraction Decomposition

Chapter 8 Summary

Chapter 8 Review Exercises

Chapter 8 Practice Test A

Chapter 8 Practice Test B

Cumulative Review Chapters P-8

9. Matrices and Determinants

9.1 Matrices and Systems of Equations

9.2 Matrix Algebra

9.3 The Matrix Inverse

9.4 Determinants and Cramer’s Rule

Chapter 9 Summary

Chapter 9 Review Exercises

Chapter 9 Practice Test A

Chapter 9 Practice Test B

Cumulative Review Chapters P-9

10. Conic Sections

10.1 Conic Sections: Overview

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

Chapter 10 Summary

Chapter 10 Review Exercises

Chapter 10 Practice Test A

Chapter 10 Practice Test B

Cumulative Review Chapters P-10

11. Further Topics in Algebra

11.1 Sequences and Series

11.2 Arithmetic Sequences; Partial Sums

11.3 Geometric Sequences and Series

11.4 Mathematical Induction

11.5 The Binomial Theorem

11.6 Counting Principles

11.7 Probability

Chapter 11 Summary

Chapter 11 Review Exercises

Chapter 11 Practice Test A

Chapter 11 Practice Test B

Cumulative Review Chapters P-11

Answers to Selected Exercises

Credits

Index of Applications

Index