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Trigonometry / Edition 3

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Overview

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.
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Product Details

  • ISBN-13: 9780470648025
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 10/4/2011
  • Series: Wiley Desktop Editions Series
  • Edition number: 3
  • Pages: 768
  • Sales rank: 409,235
  • Product dimensions: 8.20 (w) x 10.10 (h) x 1.20 (d)

Meet the Author

Cynthia Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997. Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles. In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia.
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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

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