College Algebra and Trigonometry

College Algebra and Trigonometry, Second Edition provides a comprehensive approach to the fundamental concepts and techniques of college algebra and trigonometry.

The book incorporates improvements from the previous edition to provide a better learning experience. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, trigonometric functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter contains a summary, including terms and symbols with appropriate page references; key ideas for review to stress the concepts; review exercises to provide additional practice; and progress tests to provide self-evaluation and reinforcement. The answers to all Review Exercises and Progress Tests appear in the back of the book.

College students will find the book very useful and invaluable.

Preface

Acknowledgments

To the Student

Chapter 1 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 2 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 of Quadratic Equations

2.7 Second-Degree Inequalities

Chapter 3 Functions

3.1 The Rectangular Coordinate System

3.2 Functions and Function Notation

3.3 Graphs of Functions

3.4 Linear Functions

3.5 Direct and Inverse Variation (Optional)

3.6 Combining Functions; Inverse Functions

Chapter 4 Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Fundamental Properties of Logarithms

4.4 Computing with Logarithms (Optional)

4.5 Exponential and Logarithmic Equations

Chapter 5 The Trigonometric Functions

5.0 Review of Geometry

5.1 Angles and Their Measurement

5.2 The Sine, Cosine, and Tangent Functions

5.3 Values of Sine, Cosine, and Tangent

5.4 Graphs of Sine, Cosine, and Tangent

5.5 Secant, Cosecant, and Cotangent

5.6 The Inverse Trigonometric Functions

Chapter 6 Trigonometry: Measuring Triangles

6.1 Right Triangle Trigonometry

6.2 Applications of Right Triangle Trigonometry

6.3 Law of Cosines

6.4 Law of Sines

Chapter 7 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 8 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 9 Systems of Equations and Inequalities

9.1 Systems of Equations

9.2 Solving by Elimination

9.3 Applications

9.4 Systems of Linear Equations in Three Unknowns

9.5 Systems of Linear Inequalities

9.6 Linear Programming (Optional)

Chapter 10 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 11 Theory of Polynomials

11.1 Polynomial Division and Synthetic Division

11.2 The Remainder and Factor Theorems

11.3 Factors and Zeros

11.4 Real and Rational Zeros

11.5 Rational Functions and Their Graphs

Chapter 12 Topics in Algebra

12.1 Sequences and Sigma Notation

12.2 Arithmetic Sequences

12.3 Geometric Sequences

12.4 Mathematical Induction

12.5 The Binomial Theorem

12.6 Counting: Permutations and Combinations

12.7 Probability

Tables Appendix

Answers to Odd-Numbered Exercises, and to Review Exercises and Progress Tests

Solutions to Selected Review Exercises

Index