Analytic Trigonometry with Applications, 11th Edition
November 2011, ©2012
Barnett, Analytic Trigonometry is a text that students can actually read, understand, and apply. Concept development moves from the concrete to abstract to engage the student. Almost every concept is illustrated by an example followed by a matching problem allowing students to practice knowledge precisely when they acquire it. To gain student interest quickly, the text moves directly into trigonometric concepts and applications and reviews essential material from prerequisite courses only as needed. 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 all help the student master the subject. Analytic Trigonometry 11th edition includes updated applications from a range of different fields to convince all students that trigonometry is really useful.
The seamless integration of Barnett, Analytical Trigonometry 11th edition with WileyPLUS, a research-based, online environment for effective teaching and learning, builds 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.
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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
- Exposition has been supplemented and clarified to strengthen intuition and encourage a conceptual understanding of trigonometry.
- Hundreds of new exercises have been added, including many that require a verbal explanation (marked by red problem numbers).
- Many more "reading comprehension" questions have been added to test whether the student has grasped the basic concepts of a section by an initial reading.
- In Section 2.3, a greater emphasis has been given to the unit circle in the definition of the trigonometric functions, and also in the examples that follow the definition.
- In Chapter 6, vectors are given a new, streamlined treatment.
- Wide variety of applications: Most sections contain applied exercises from astronomy, physics, engineering, and the life sciences. There are a wide variety and ample number of up-to-date applications distributed through-out the text to convince the most skeptical students that mathematics is really useful.
- Contains over 180 numbered worked examples with annotated solution steps. Each concept is illustrated with one or more examples, and following each example is a PARALLEL or "MATCHED" problem with an answer near the end of the section so that a student can immediately check his or understanding of a concept.
- Over 3,000 carefully selected and graduated problems, progressing from skill/drill exercises through intermediate and challenging exercises.
- Graphing utility activities are included in appropriate places in the book. These include brief discussions in the text, examples or portions of examples solved on a graphing utility, and problems for the student to solve.
- Explore-Discuss boxes are interspersed in every section at appropriate places to encourage a student to think about a relationship or process before a result is stated or to investigate additional consequences of a development in the text.
- Group activities are included at the end of every chapter and involve a number of the concepts discussed in the chapter.
- WileyPLUS, accompanied with Barnett, Analytical Trigonometry 11th edition, provides a research based, online environment for effective teaching and learning. 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.
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