# College Algebra and Trigonometry A Unit Circle Approach

**by**Dugopolski, Mark

### 9780321644770

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## Summary

## Author Biography

**Mark Dugopolski** was born in Menominee, Michigan. After receiving a BS from Michigan State University, he taught high school in Illinois for four years. He received an M.S. in mathematics from Northern Illinois University at DeKalb. He then received a PhD in the area of topology and an MS in statistics from the University of Illinois at Champaign–Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for twenty-five years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.

## Table of Contents

**P. Prerequisites**

P.1 Real Numbers and Their Properties

P.2 Integral Exponents and Scientific Notations

P.3 Rational Exponents and Radicals

P.4 Polynomials

P.5 Factoring Polynomials

P.6 Rational Expressions

P.7 Complex Numbers

Chapter P Highlights

Chapter P Review Exercises

Chapter P Test

**1. Equations, Inequalities, and Modeling**

1.1 Equations in One Variable

1.2 Constructing Models to Solve Problems

1.3 Equations and Graphs in Two Variables

1.4 Linear Equations in Two Variables

1.5 Scatter Diagrams and Curve Fitting

1.6 Quadratic Equations

1.7 Linear and Absolute Value Inequalities

Chapter 1 Highlights

Chapter 1 Review Exercises

Chapter 1 Test

Tying it all Together

**2. Functions and Graphs**

2.1 Functions

2.2 Graphs of Relations and Functions

2.3 Families of Functions, Transformations, and Symmetry

2.4 Operations with Functions

2.5 Inverse Functions

2.6 Constructing Functions with Variation

Chapter 2 Highlights

Chapter 2 Review Exercises

Chapter 2 Test

Tying it all Together

**3. Polynomial and Rational Functions**

3.1 Quadratic Functions and Inequalities

3.2 Zeros of Polynomial Functions

3.3 The Theory of Equations

3.4 Miscellaneous Equations

3.5 Graphs of Polynomial Functions

3.6 Rational Functions and Inequalities

Chapter 3 Highlights

Chapter 3 Review Exercises

Chapter 3 Test

Tying it all Together

**4. Exponential and Logarithmic Functions**

4.1 Exponential Functions and Their Applications

4.2 Logarithmic Functions and Their Applications

4.3 Rules of Logarithms

4.4 More Equations and Applications

Chapter 4 Highlights

Chapter 4 Review Exercises

Chapter 4 Test

Tying it all Together

**5. The Trigonometric Functions**

5.1 Angles and Their Measurements

5.2 The Sine and Cosine Functions

5.3 The Graphs of the Sine and Cosine Functions

5.4 The Other Trigonometric Functions and Their Graphs

5.5 The Inverse Trigonometric Functions

5.6 Right Triangle Trigonometry

Chapter 5 Highlights

Chapter 5 Review Exercises

Chapter 5 Test

Tying it all Together

**6. Trigonometric Identities and Conditional Equations**

6.1 Basic Identities

6.2 Verifying Identities

6.3 Sum and Difference Identities

6.4 Double-Angle and Half-Angle Identities

6.5 Product and Sum Identities

6.6 Conditional Trigonometric Equations

Chapter 6 Highlights

Chapter 6 Review Exercises

Chapter 6 Test

Tying it all Together

**7. Applications of Trigonometry**

7.1 The Law of Sines

7.2 The Law of Cosines

7.3 Vectors

7.4 Trigonometric Form of Complex Numbers

7.5 Powers and Roots of Complex Numbers

7.6 Polar Coordinates (Equations???)

7.7 Parametric Equations

Chapter 7 Highlights

Chapter 7 Review Exercises

Chapter 7 Test

Tying it all Together

**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 Nonlinear Systems of Equations

8.4 Partial Fractions

8.5 Inequalities and Systems of Inequalities in Two Variables

8.6 The Linear Programming Model

Chapter 8 Highlights

Chapter 8 Review Exercises

Chapter 8 Test

Tying it all Together

**9. Matrices and Determinants**

9.1 Solving Linear Systems Using Matrices

9.2 Operations with Matrices

9.3 Multiplication of Matrices

9.4 Inverses of Matrices

9.5 Solutions of Linear Systems in Two Variables Using Determinants

9.6 Solutions of Linear Systems in Three Variables Using Determinants

Chapter 9 Highlights

Chapter 9 Review Exercises

Chapter 9 Test

Tying it all Together

**10. The Conic Sections**

10.1 The Parabola

10.2 The Ellipse and the Circle

10.3 The Hyperbola

Chapter 10 Highlights

Chapter 10 Review Exercises

Chapter 10 Test

Tying it all Together

**11. Sequences, Series, and Probability**

11.1 Sequences

11.2 Series

11.3 Geometric Sequences and Series

11.4 Counting and Permutations

11.5 Combinations, Labeling, and the Binomial Theorem

11.6 Probability

11.7 Mathematical Induction

Chapter 11 Highlights

Chapter 11 Review Exercises

Chapter 11 Test

Appendix: Solutions to “Try This” Exercises

Answers

Credits

Index of Applications

Index