Trigonometry, Binder Ready Version

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 what to do, how to do it, and whether they did it right. WileyPLUS sold separately from text. Copyright......Page 6 About the Author......Page 9 Preface......Page 10 Trigonometry......Page 5 Table of Contents......Page 18 A Note from the Author to the Student......Page 21 1: Right Triangle Trigonometry......Page 30 1.1: Angles, Degrees, and Triangles......Page 32 1.2: Similar Triangles......Page 45 1.3: Definition 1 of Trigonometric Functions: Right Triangle Ratios......Page 56 1.4: Evaluating Trigonometric Functions: Exactly and with Calculators......Page 66 1.5: Solving Right Triangles......Page 77 Inquiry-Based Learning Project......Page 91 Modeling Our World......Page 93 Review......Page 95 Review Exercises......Page 98 Practice Test......Page 101 2: Trigonometric Functions......Page 102 2.1: Angles in the Cartesian Plane......Page 104 2.2: Definition 2 of Trigonometric Functions: The Cartesian Plane......Page 112 2.3: Evaluating Trigonometric Functions for Nonacute Angles......Page 121 2.4: Basic Trigonometric Identities......Page 138 Inquiry-Based Learning Project......Page 148 Modeling Our World......Page 149 Review......Page 150 Review Exercises......Page 152 Practice Test......Page 154 Cumulative Test......Page 155 3: Radian Measure and the Unit Circle Approach......Page 156 3.1: Radian Measure......Page 158 3.2: Arc Length and Area of a Circular Sector......Page 169 3.3: Linear and Angular Speeds......Page 179 3.4: Definition 3 of Trigonometric Functions: Unit Circle Approach......Page 187 Inquiry-Based Learning Project......Page 198 Modeling Our World......Page 199 Review......Page 200 Review Exercises......Page 202 Practice Test......Page 204 Cumulative Test......Page 205 4: Graphing Trigonometric Functions......Page 206 4.1: Basic Graphs of Sine and Cosine Functions: Amplitude and Period......Page 208 4.2: Translations of the Sine and Cosine Functions: Addition of Ordinates......Page 232 4.3: Graphs of Tangent, Cotangent, Secant, and Cosecant Functions......Page 254 Inquiry-Based Learning Project......Page 274 Modeling Our World......Page 275 Review......Page 276 Review Exercises......Page 279 Practice Test......Page 282 Cumulative Test......Page 283 5: Trigonometric Identities......Page 284 5.1: Trigonometric Identities......Page 286 5.2: Sum and Difference Identities......Page 296 5.3: Double-Angle Identities......Page 309 5.4: Half-Angle Identities......Page 318 5.5: Product-to-Sum and Sum-to-Product Identities......Page 328 Inquiry-Based Learning Project......Page 337 Modeling Our World......Page 338 Review......Page 339 Review Exercises......Page 341 Practice Test......Page 344 Cumulative Test......Page 345 6: Solving Trigonometric Equations......Page 346 6.1: Inverse Trigonometric Functions......Page 348 6.2: Solving Trigonometric Equations That Involve Only One Trigonometric Function......Page 370 6.3: Solving Trigonometric Equations That Involve Multiple Trigonometric Functions......Page 381 Inquiry-Based Learning Project......Page 388 Modeling Our World......Page 390 Review......Page 391 Review Exercises......Page 394 Practice Test......Page 396 Cumulative Test......Page 397 7: Applications of Trigonometry: Triangles and Vectors......Page 398 7.1: Oblique Triangles and the Law of Sines......Page 400 7.2: The Law of Cosines......Page 415 7.3: The Area of a Triangle......Page 425 7.4: Vectors......Page 433 7.5: The Dot Product......Page 449 Inquiry-Based Learning Project......Page 457 Modeling Our World......Page 458 Review......Page 459 Review Exercises......Page 461 Practice Test......Page 464 Cumulative Test......Page 465 8: Complex Numbers, Polar Coordinates, and Parametric Equations......Page 466 8.1: Complex Numbers......Page 468 8.2: Polar (Trigonometric) Form of Complex Numbers......Page 475 8.3: Products, Quotients, Powers, and Roots of Complex Numbers: De Moivre's Theorem......Page 484 8.4: Polar Equations and Graphs......Page 497 8.5: Parametric Equations and Graphs......Page 511 Inquiry-Based Learning Project......Page 522 Modeling Our World......Page 523 Review......Page 525 Review Exercises......Page 527 Practice Test......Page 529 Cumulative Test......Page 530 Appendix A: Algebraic Prerequisites and Review......Page 531 A.1: Factoring Polynomials......Page 532 A.2: Basic Tools: Cartesian Plane, Distance, and Midpoint......Page 543 A.3: Graphing Equations: Point-Plotting, Intercepts, and Symmetry......Page 551 A.4: Functions......Page 563 A.5: Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change......Page 582 A.6: Graphing Techniques: Transformations......Page 602 A.7: Operations on Functions and Composition of Functions......Page 617 A.8: One-to-One Functions and Inverse Functions......Page 627 Review......Page 642 Review Exercises......Page 645 Practice Test......Page 649 Appendix B: Conic Sections......Page 651 B.1: Conic Basics......Page 652 B.2: The Parabola......Page 655 B.3: The Ellipse......Page 668 B.4: The Hyperbola......Page 680 B.5: Rotation of Axes......Page 692 B.6: Polar Equations of Conics......Page 702 Review......Page 713 Review Exercises......Page 716 Practice Test......Page 719 Answers to Odd Numbered Exercises......Page 720 Applications Index......Page 766 Subject Index......Page 768 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, single 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 Cynthia Young's 3rd Edition of Trigonometry focuses on revisions and additions including hundreds of new exercises, more opportunities to use technology, and themed modeling projects that help connect content to real-world issues. The text builds upon the previous two editions with more in-depth and enhanced coverage on ways to help overcome common learning barriers in trigonometry and build confidence for readers. The text features truly unique, strong pedagogy and as with the previous two issues, is written in a clear, single voice.