Algebra and Trigonometry

About the Author v

Preface to the Instructor xvi

WileyPLUS xxii

Acknowledgments xxiii

Preface to the Student xxvi

1 The Real Numbers 1

1.1 The Real Line 2

1.2 Algebra of the Real Numbers 7

1.3 Inequalities, Intervals, and Absolute Value 24

2 Combining Algebra and Geometry 41

2.1 The Coordinate Plane 42

2.2 Lines 57

2.3 Quadratic Expressions and Conic Sections 75

2.4 Area 98

3 Functions and Their Graphs 117

3.1 Functions 118

3.2 Function Transformations and Graphs 142

3.3 Composition of Functions 165

3.4 Inverse Functions 180

3.5 A Graphical Approach to Inverse Functions 197

4 Polynomial and Rational Functions 213

4.1 Integer Exponents 214

4.2 Polynomials 227

4.3 Rational Functions 245

4.4 Complex Numbers 262

5 Exponents and Logarithms 279

5.1 Exponents and Exponential Functions 280

5.2 Logarithms as Inverses of Exponential Functions 293

5.3 Applications of Logarithms 310

5.4 Exponential Growth 328

6 e and the Natural Logarithm 349

6.1 Defining e and ln 350

6.2 Approximations and area with e and ln 366

6.3 Exponential Growth Revisited 376

7 Systems of Equations 387

7.1 Equations and Systems of Equations 388

7.2 Solving Systems of Linear Equations 399

7.3 Solving Systems of Linear Equations Using Matrices 411

7.4 Matrix Algebra 424

8 Sequences, Series, and Limits 447

8.1 Sequences 448

8.2 Series 463

8.3 Limits 483

9 Trigonometric Functions 497

9.1 The Unit Circle 498

9.2 Radians 514

9.3 Cosine and Sine 529

9.4 More Trigonometric Functions 542

9.5 Trigonometry in Right Triangles 555

9.6 Trigonometric Identities 566

10 Trigonometric Algebra and Geometry 583

10.1 Inverse Trigonometric Functions 584

10.2 Inverse Trigonometric Identities 599

10.3 Using Trigonometry to Compute Area 613

10.4 The Law of Sines and the Law of Cosines 628

10.5 Double-Angle and Half-Angle Formulas 644

10.6 Addition and Subtraction Formulas 658

11 Applications of Trigonometry 671

11.1 Parametric Curves 672

11.2 Transformations of Trigonometric Functions 687

11.3 Polar Coordinates 705

11.4 Vectors 718

11.5 The Complex Plane 732

Photo Credits 743

Index 745