| |
| |
| Preface | |
| |
| |
| |
| Measurement of Angles, Arcs and Sectors | |
| |
| |
| |
| Using Radians, Degrees, or Grads to Measure Angles | |
| |
| |
| |
| Length of an Arc and Area of a Sector of a Circle | |
| |
| |
| |
| Circular Motion | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| The Trigonometric Functions | |
| |
| |
| |
| Definition of the Six Trigonometric Functions | |
| |
| |
| |
| Values of the Trigonometric Functions for 0, 30, 45, 60, 90, 180 degree Angles | |
| |
| |
| |
| Trigonometric Functions for Right Triangles | |
| |
| |
| |
| Solving Right Triangles | |
| |
| |
| |
| Applications of Right Triangle Trigonometry | |
| |
| |
| |
| Circular Functions | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Graphs of the Trigonometric Functions | |
| |
| |
| |
| Graphing Generic Sine and Cosine Functions | |
| |
| |
| |
| Shifting Generic Curves Right/Left or Up/Down | |
| |
| |
| |
| Using the Graphing Calculator to Graph Functions by Addition of Ordinates | |
| |
| |
| |
| Graphing the Tangent and Cotangent Functions | |
| |
| |
| |
| Graphing the Secant and Cosecant Functions | |
| |
| |
| |
| Qualitative Analysis of Trigonometric Functions | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Inverse Trigonometric Functions | |
| |
| |
| |
| Relations, Functions, and Their Inverses | |
| |
| |
| |
| Inverse of the Trigonometric Functions | |
| |
| |
| |
| Finding Inverses of Trigonometric Functions Using a Calculator | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Basic Trigonometric Identities | |
| |
| |
| |
| Fundamental Identities | |
| |
| |
| |
| Opposite Angle Identities | |
| |
| |
| |
| Additional Techniques to Prove Identities | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Sum and Difference Identities | |
| |
| |
| |
| Sum and Difference Formulas for Cosine | |
| |
| |
| |
| Some Identities Useful in Calculus | |
| |
| |
| |
| Tan ( � �) | |
| |
| |
| |
| Identities Involving Sums and Differences of n or +n | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| Chapters 1-6 Cumulative Review | |
| |
| |
| |
| Additional Identities | |
| |
| |
| |
| Double-Angle Identities | |
| |
| |
| |
| Half-Angle Identities | |
| |
| |
| |
| Identities to Rewrite Sums and Products | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Trigonometric Equations | |
| |
| |
| |
| Solving Basic Trigonometric Equations | |
| |
| |
| |
| Solving Trigonometric Equations Involving Factoring | |
| |
| |
| |
| Solving Trigonometric Equations Where the Argument is a Function | |
| |
| |
| |
| Using Identities to Solve Trigonometric Equations | |
| |
| |
| |
| Applications | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Laws of Sines and Law of Cosines | |
| |
| |
| |
| Derivation of the Law of Sines | |
| |
| |
| |
| The Ambiguous Case | |
| |
| |
| |
| Applications of the Law of Sines | |
| |
| |
| |
| Derivations of the Law of Cosines | |
| |
| |
| |
| Applications of the Law of Cosines | |
| |
| |
| |
| Area of a Triangle | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Vectors | |
| |
| |
| |
| Addition of Vectors | |
| |
| |
| |
| Geometric Resolution of Vectors | |
| |
| |
| |
| Algebraic Resolution of Vectors | |
| |
| |
| |
| Work, Inclined Planes, and the Dot Product | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Complex Numbers | |
| |
| |
| |
| Algebraic Operations with Complex Numbers | |
| |
| |
| |
| Trigonometric and Polar Representation of Complex Numbers | |
| |
| |
| |
| DeMoivre's Theorem | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| |
| Polar Coordinates | |
| |
| |
| |
| The Polar Coordinate System | |
| |
| |
| |
| Parametric Equations | |
| |
| |
| |
| Other Curves in Polar Coordinates | |
| |
| |
| Key Ideas | |
| |
| |
| Review Test | |
| |
| |
| Chapters 1-12 Cumulative Review | |
| |
| |
| Appendix Rounding Off and Significant Figures | |
| |
| |
| Selected Answers | |
| |
| |
| Index | |