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Summary
Summary
This text is designed for an in-depth course in trigonometry. Although the development of trigonometry begins on page one, the authors realize that many students may have completed algebra and geometry courses some time ago. Therefore, they have included algebra and geometry reminders throughout the text where they know from their teaching experience that many students need help in recalling ideas that are necessary to develop trigonometry. While it assumes no previous knowledge of trigonometry, this book shows how trigonometry can be used in many fields. It also develops algebra skills so that students will be thoroughly prepared to continue their study of mathematics and science. The use of graphing calculators has been incorporated throughout the text to reduce the labor of calculations and to expand the students' understanding of concepts and give students the opportunity to explore relationships. A Student Solutions Manual is available for sale. Additionally, an Instructor Solutions Manual is available for teachers by emailing shirley_grall@mcgraw-hill.com
Table of Contents
| Preface |
| Chapter 1 Measurement of Angles, Arcs and Sectors |
| 1-1 Using Radians, Degrees, or Grads to Measure Angles |
| 1-2 Length of an Arc and Area of a Sector of a Circle |
| 1-3 Circular Motion |
| Key Ideas |
| Review Test |
| Chapter 2 The Trigonometric Functions |
| 2-1 Definition of the Six Trigonometric Functions |
| 2-2 Values of the Trigonometric Functions for 0, 30, 45, 60, 90, 180 degree Angles |
| 2-3 Trigonometric Functions for Right Triangles |
| 2-4 Solving Right Triangles |
| 2-5 Applications of Right Triangle Trigonometry |
| 2-6 Circular Functions |
| Key Ideas |
| Review Test |
| Chapter 3 Graphs of the Trigonometric Functions |
| 3-1 Graphing Generic Sine and Cosine Functions |
| 3-2 Shifting Generic Curves Right/Left or Up/Down |
| 3-3 Using the Graphing Calculator to Graph Functions by Addition of Ordinates |
| 3-4 Graphing the Tangent and Cotangent Functions |
| 3-5 Graphing the Secant and Cosecant Functions |
| 3-6 Qualitative Analysis of Trigonometric Functions |
| Key Ideas |
| Review Test |
| Chapter 4 Inverse Trigonometric Functions |
| 4-1 Relations, Functions, and Their Inverses |
| 4-2 Inverse of the Trigonometric Functions |
| 4-3 Finding Inverses of Trigonometric Functions Using a Calculator |
| Key Ideas |
| Review Test |
| Chapter 5 Basic Trigonometric Identities |
| 5-1 Fundamental Identities |
| 5-2 Opposite Angle Identities |
| 5-3 Additional Techniques to Prove Identities |
| Key Ideas |
| Review Test |
| Chapter 6 Sum and Difference Identities |
| 6-1 Sum and Difference Formulas for Cosine |
| 6-2 Some Identities Useful in Calculus |
| 6-3 Tan ( ¦ ¯) |
| 6-4 Identities Involving Sums and Differences of n or +n |
| Key Ideas |
| Review Test |
| Chapters 1-6 Cumulative Review |
| Chapter 7 Additional Identities |
| 7-1 Double-Angle Identities |
| 7-2 Half-Angle Identities |
| 7-3 Identities to Rewrite Sums and Products |
| Key Ideas |
| Review Test |
| Chapter 8 Trigonometric Equations |
| 8-1 Solving Basic Trigonometric Equations |
| 8-2 Solving Trigonometric Equations Involving Factoring |
| 8-3 Solving Trigonometric Equations Where the Argument is a Function |
| 8-4 Using Identities to Solve Trigonometric Equations |
| 8-5 Applications |
| Key Ideas |
| Review Test |
| Chapter 9 Laws of Sines and Law of Cosines |
| 9-1 Derivation of the Law of Sines |
| 9-2 The Ambiguous Case |
| 9-3 Applications of the Law of Sines |
| 9-4 Derivations of the Law of Cosines |
| 9-5 Applications of the Law of Cosines |
| 9-6 Area of a Triangle |
| Key Ideas |
| Review Test |
| Chapter 10 Vectors |
| 10-1 Addition of Vectors |
| 10-2 Geometric Resolution of Vectors |
| 10-3 Algebraic Resolution of Vectors |
| 10-4 Work, Inclined Planes, and the Dot Product |
| Key Ideas |
| Review Test |
| Chapter 11 Complex Numbers |
| 11-1 Algebraic Operations with Complex Numbers |
| 11-2 Trigonometric and Polar Representation of Complex Numbers |
| 11-3 DeMoivre's Theorem |
| Key Ideas |
| Review Test |
| Chapter 12 Polar Coordinates |
| 12-1 The Polar Coordinate System |
| 12-2 Parametric Equations |
| 12-3 Other Curves in Polar Coordinates |
| Key Ideas |
| Review Test |
| Chapters 1-12 Cumulative Review |
| Appendix Rounding Off and Significant Figures |
| Selected Answers |
| Index |
