# Trigonometry, 3rd Edition

# Trigonometry, 3rd Edition

ISBN: 978-1-118-21023-9

Dec 2011

768 pages

## Description

The third edition of Cynthia Young's Trigonometry brings together all the elements that have allowed instructors and learners to successfully "bridge the gap" between classroom instruction and independent homework by overcoming common learning barriers and building confidence in students' ability to do mathematics. Written in a clear voice that speaks to students and mirrors how instructors communicate in lecture, Young's hallmark pedagogy enables students to become independent, successful learners. Varied exercise types and modeling projects keep the learning fresh and motivating. Young continues her tradition of fostering a love for succeeding in mathematics by introducing inquiry-based learning projects in this edition, providing learners an opportunity to master the material with more freedom while reinforcing mathematical skills and intuition.

The seamless integration of Cynthia Young's Trigonometry 3rd edition with WileyPLUS, a research-based, online environment for effective teaching and learning, continues Young's vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right.

WileyPLUS sold separately from text.

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**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**

**New Applications Added:**Applications to Economics, Business, Environmental Science, and Health have been added to each chapter to augment existing applications on Finance, Biology, and Chemistry.**Inquiry-Based Learning Projects added to every chapter!**These projects actively involve students in the learning process, aiding in understanding and mastery of the material.**Revised and Enriched Exercise Sets Throughout****Updated “Technology Tips”:**Optional technology tips in the margin demonstrate how students can use technology to confirm analytic solutions.

**Clear, Concise and Inviting Writing.**The author's engaging and clear presentation is presented in a layout that is designed to reduce math anxiety in students.**Author Lecture Videos.**For review at home or for a class missed, Cynthia Young has recorded over 300 instructional videos including worked examples and "Your Turn" problems from the text. These videos can be found in Wiley*PLUS*and are denoted in the text with an icon., accompanied with*WileyPLUS***Young,***Trigonometry*, provides a research based, online environment for effective teaching and learning.*3*^{rd}edition*WileyPLUS*builds students’ confidence because it takes the guesswork out of studying by providing students with a clear roadmap: what to do, how to do it, if they did it right.**Six Different Types of Exercises.**Every chapter has skill, application, catch the mistake, challenge, conceptual, and technology exercises. The exercises gradually increase in difficulty and vary skill and conceptual emphasis.**Correct vs. Incorrect.**In addition to standard examples, some problems are worked both correctly and incorrectly to highlight common errors students make. Counter examples, like these, are often an effective learning approach for many students.**Catch the Mistake.**In every section, ‘Catch the Mistake’ exercises put the students in the role of the instructor grading homework which increases the depth of understanding and reinforces what they have learned.**Your Turn.**Students are often asked to work a problem immediately following an example to reinforce and check their understanding. This helps them build confidence as they progress in the chapter. These are ideal for in-class activity and preparing the student to work homework later.**Parallel Words and Math.**This text reverses the common presentation of examples by placing the explanation in words*on the left*and the mathematics in parallel*on the right*. This makes it easier for students to read through examples as the material flows more naturally and as commonly presented in lecture.**Modeling Our World.**Found in every chapter, these projects engage students by using real world data to model mathematical applications found in everyday life.**Chapter Cumulative Test.**Included at the end of each chapter to assess and improve students' retention of material.