Analytic Trigonometry with Applications / Edition 11

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Overview

The 11th edition of Analytic Trigonometry continues to offer readers trigonometric concepts and applications. Almost every concept is illustrated by an example followed by a matching problem to encourage an active involvement in the learning process, and concept development proceeds from the concrete to the abstract. Extensive chapter review summaries, chapter and cumulative review exercises with answers keyed to the corresponding text sections, effective use of color comments and annotations, and prominent displays of important material to help master the subject. Analytic Trigonometry, 11e includes updated applications from a range of different fields.
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Editorial Reviews

Booknews
A new edition of a trigonometry textbook. Chapters cover identities, graphing functions, trigonometric equations and inequalities, triangles and vectors, and polar coordinates. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780470648056
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 11/22/2011
  • Edition description: New Edition
  • Edition number: 11
  • Pages: 624
  • Sales rank: 170,381
  • Product dimensions: 8.21 (w) x 9.94 (h) x 1.21 (d)

Meet the Author

Raymond A. Barnett, a native of and educated in California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Associated with four different publishers, Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish. Co-authors include Michael Ziegler, Marquette University; Thomas Kearns, Northern Kentucky University; Charles Burke, City College of San Francisco; John Fujii, Merritt College, and Karl Byleen, Marquette University.

Michael R. Ziegler received his B.S. from Shippensburg State College and his M.S. and Ph.D. from the University of Delaware. After completing postdoctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler has published over a dozen research articles in complex analysis and has co-authored over a dozen undergraduate mathematics textbooks with Raymond Barnett and Karl Byleen.

Karl E. Byleen received the B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups.

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Table of Contents

1 RIGHT TRIANGLE RATIOS 1

1.1 Angles, Degrees, and Arcs 2

1.2 Similar Triangles 13

1.3 Trigonometric Ratios and Right Triangles 22

1.4 Right Triangle Applications 33

Chapter 1 Group Activity: A Logistics Problem 44

Chapter 1 Review 45

2 TRIGONOMETRIC FUNCTIONS 51

2.1 Degrees and Radians 52

2.2 Linear and Angular Velocity 65

2.3 Trigonometric Functions: Unit Circle Approach 72

2.4 Additional Applications 84

2.5 Exact Values and Properties of Trigonometric Functions 98

Chapter 2 Group Activity: Speed of Light in Water 112

Chapter 2 Review 114

3 GRAPHING TRIGONOMETRIC FUNCTIONS 121

3.1 Basic Graphs 123

3.2 Graphing and 138

3.3 Graphing and 157

3.4 Additional Applications 172

3.5 Graphing the Sum of Functions 187

3.6 Tangent, Cotangent, Secant, and Cosecant Functions Revisited 199

Chapter 3 Group Activity: Predator–Prey Analysis Involving Coyotes and Rabbits 211

Chapter 3 Review 212

Cumulative Review Exercise, Chapters 1–3 220

4 IDENTITIES 227

4.1 Fundamental Identities and Their Use 228

4.2 Verifying Trigonometric Identities 235

4.3 Sum, Difference, and Cofunction Identities 245

4.4 Double-Angle and Half-Angle Identities 256

4.5 Product–Sum and Sum–Product Identities 267

Chapter 4 Group Activity: From to 275

Chapter 4 Review 277

5 INVERSE TRIGONOMETRIC FUNCTIONS; TRIGONOMETRIC EQUATIONS AND INEQUALITIES 285

5.1 Inverse Sine, Cosine, and Tangent Functions 286

5.2 Inverse Cotangent, Secant, and Cosecant Functions 307

5.3 Trigonometric Equations: An Algebraic Approach 314

5.4 Trigonometric Equations and Inequalities: A Graphing Calculator Approach 327

Chapter 5 Group Activity: and 336

Chapter 5 Review 337

Cumulative Review Exercise, Chapters 1–5 343

6 ADDITIONAL TOPICS: TRIANGLES AND VECTORS 349

6.1 Law of Sines 350

6.2 Law of Cosines 365

6.3 Areas of Triangles 376

6.4 Vectors 383

6.5 The Dot Product 399

Chapter 6 Group Activity: The SSA Case and the Law of Cosines 409

Chapter 6 Review 410

7 POLAR COORDINATES; COMPLEX NUMBERS 421

7.1 Polar and Rectangular Coordinates 422

7.2 Sketching Polar Equations 431

7.3 The Complex Plane 444

7.4 De Moivre’s Theorem and the nth-Root Theorem 453

Chapter 7 Group Activity: Orbits of Planets 461

Chapter 7 Review 463

Cumulative Review Exercise, Chapters 1–7 467

Appendix A COMMENTS ON NUMBERS 473

A.1 Real Numbers 474

A.2 Complex Numbers 477

A.3 Significant Digits 481

Appendix B FUNCTIONS AND INVERSE FUNCTIONS 489

B.1 Functions 490

B.2 Graphs and Transformations 497

B.3 Inverse Functions 508

Appendix C PLANE GEOMETRY: SOME USEFUL FACTS 515

C.1 Lines and Angles 516

C.2 Triangles 517

C.3 Quadrilaterals 519

C.4 Circles 520

Selected Answers A-1

Index I-1

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