# Analytic Trigonometry with Applications, 11th Edition

# Analytic Trigonometry with Applications, 11th Edition

ISBN: ES8-0-470-64805-6

## Description

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 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 *n*th-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

- 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., accompanied with*WileyPLUS***Barnett,**, provides a research based, online environment for effective teaching and learning.*Analytical Trigonometry 11*^{th}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.