## Table of contents

**1 Right Triangle Trigonometry 2**

**1.1** Angles, Degrees, and Triangles 4

**1.2** Similar Triangles 17

**1.3** Definition 1 of Trigonometric Functions: Right Triangle Ratios 28

**1.4** Evaluating Trigonometric Functions: Exactly and with Calculators 38

**1.5** Solving Right Triangles 49

**Inquiry-Based Learning Project** 63 | **Modeling Our World** 65 |

**Review** 67 | **Review Exercises** 70 | **Practice Test** 73

**2 Trigonometric Functions 74**

**2.1** Angles in the Cartesian Plane 76

**2.2** Definition 2 of Trigonometric Functions: The Cartesian Plane 84

**2.3** Evaluating Trigonometric Functions for Nonacute Angles 93

**2.4** Basic Trigonometric Identities 110

**Inquiry-Based Learning Project** 120 | **Modeling Our World** 121 |

**Review** 122 | **Review Exercises** 124 | **Practice Test** 126 |

**Cumulative Test** 127

**3 Radian Measure and the Unit Circle Approach 128**

**3.1** Radian Measure 130

**3.2** Arc Length and Area of a Circular Sector 141

**3.3** Linear and Angular Speeds 151

**3.4** Definition 3 of Trigonometric Functions: Unit Circle Approach 159

**Inquiry-Based Learning Project** 170 | **Modeling Our World** 171 |

**Review** 172 | **Review Exercises** 174 | **Practice Test** 176 |

**Cumulative Test** 177

**4 Graphing Trigonometric Functions 178**

**4.1** Basic Graphs of Sine and Cosine Functions: Amplitude and Period 180

**4.2** Translations of the Sine and Cosine Functions: Addition of Ordinates 204

**4.3** Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 226

**Inquiry-Based Learning Project** 246 | **Modeling Our World** 247 |

**Review** 248 | **Review Exercises** 251 | **Practice Test** 254 |

**Cumulative Test** 255

**5 Trigonometric Identities 256**

**5.1** Trigonometric Identities 258

**5.2** Sum and Difference Identities 268

**5.3** Double-Angle Identities 281

**5.4** Half-Angle Identities 290

**5.5** Product-to-Sum and Sum-to-Product Identities 300

**Inquiry-Based Learning Project** 309 | **Modeling Our World** 310 |

**Review** 311 | **Review Exercises** 313 | **Practice Test** 316 |

**Cumulative Test** 317

**6 Solving Trigonometric Equations 318**

**6.1** Inverse Trigonometric Functions 320

**6.2** Solving Trigonometric Equations That Involve Only One Trigonometric Function 342

**6.3** Solving Trigonometric Equations That Involve Multiple Trigonometric Functions 353

**Inquiry-Based Learning Project** 360 | **Modeling Our World** 362 |

**Review** 363 | **Review Exercises** 366 | **Practice Test** 368 |

**Cumulative Test** 369

**7 Applications of Trigonometry: Triangles and Vectors 370**

**7.1** Oblique Triangles and the Law of Sines 372

**7.2** The Law of Cosines 387

**7.3** The Area of a Triangle 397

**7.4** Vectors 405

**7.5** The Dot Product 421

**Inquiry-Based Learning Project** 429 | **Modeling Our World** 430 |

**Review** 431 | **Review Exercises** 433 | **Practice Test** 436 |

**Cumulative Test** 437

**8 Complex Numbers, Polar Coordinates, and Parametric Equations 438**

**8.1** Complex Numbers 440

**8.2** Polar (Trigonometric) Form of Complex Numbers 447

**8.3** Products, Quotients, Powers, and Roots of Complex Numbers: De Moivre’s Theorem 456

**8.4** Polar Equations and Graphs 469

**8.5** Parametric Equations and Graphs 483

**Inquiry-Based Learning Project** 494 | **Modeling Our World** 495 |

**Review** 497 | **Review Exercises** 499 | **Practice Test** 501 |

**Cumulative Test** 502

**Appendix A Algebraic Prerequisites and Review 503**

**A.1** Factoring Polynomials 504

**A.2** Basic Tools: Cartesian Plane, Distance, and Midpoint 515

**A.3** Graphing Equations: Point-Plotting, Intercepts, and Symmetry 523

**A.4** Functions 535

**A.5** Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 554

**A.6** Graphing Techniques: Transformations 574

**A.7** Operations on Functions and Composition of Functions 589

**A.8** One-to-One Functions and Inverse Functions 599

**Review** 614 | **Review Exercises** 617 | **Practice Test** 621

**Appendix B Conic Sections 623**

**B.1** Conic Basics 624

**B.2** The Parabola 627

**B.3** The Ellipse 640

**B.4** The Hyperbola 652

**B.5** Rotation of Axes 664

**B.6** Polar Equations of Conics 674

**Review** 685 | **Review Exercises** 688 | **Practice Test** 691

**Answers to Odd Numbered Exercises 692**

**Applications Index 738**

**Subject Index 740**