Trigonometry

Preface......Page 5
Contents......Page 7
1.1 Angles......Page 9
1.2 Trigonometric Functions of an Acute Angle......Page 15
1.3 Applications and Solving Right Triangles......Page 22
1.4 Trigonometric Functions of Any Angle......Page 32
1.5 Rotations and Reflections of Angles......Page 40
2.1 The Law of Sines......Page 46
2.2 The Law of Cosines......Page 52
2.3 The Law of Tangents......Page 59
2.4 The Area of a Triangle......Page 62
2.5 Circumscribed and Inscribed Circles......Page 67
3.1 Basic Trigonometric Identities......Page 73
3.2 Sum and Difference Formulas......Page 79
3.3 Double-Angle and Half-Angle Formulas......Page 86
3.4 Other Identities......Page 90
4.1 Radians and Degrees......Page 95
4.2 Arc Length......Page 98
4.3 Area of a Sector......Page 103
4.4 Circular Motion: Linear and Angular Speed......Page 108
5.1 Graphing the Trigonometric Functions......Page 111
5.2 Properties of Graphs of Trigonometric Functions......Page 117
5.3 Inverse Trigonometric Functions......Page 128
6.1 Solving Trigonometric Equations......Page 137
6.2 Numerical Methods in Trigonometry......Page 141
6.3 Complex Numbers......Page 147
6.4 Polar Coordinates......Page 154
Appendix A: Answers and Hints to Selected Exercises......Page 160
Appendix B: Graphing with Gnuplot......Page 163
GNU Free Documentation License......Page 168
History......Page 176
Index......Page 177