Table of Contents
Introduction 1
Common Core State Standards for Mathematics (CCSSM) 1
Connecting to Common Core Mathematics 2
Why You Need This Book 3
How to Use This Book 3
Hundreds of Practice Questions Online! 4
Chapter 1 Geometric Prerequisites 5
Congruence 6
Dilation 7
Similarity 8
Pythagorean Theorem 8
Chapter 2 Trigonometric Numbers of Angles 11
Angles 12
Sine and Cosine Numbers of Acute Angles 18
Sine and Cosine Numbers of an Acute Angle of a Right Triangle 20
Sine and Cosine Numbers of Any Angles 23
The Unit Circle 25
Sine and Cosine Numbers of Special Angles 29
Tangent, Cosecant, Secant, and Cotangent Numbers of Angles 38
Chapter 3 Trigonometric Functions 43
Sine Function 44
Cosine Function 48
General Sine and Cosine Functions 49
Tangent Function 64
Cosecant Function 67
Secant Function 69
Cotangent Function 71
Chapter 4 Inverse Trigonometric Functions 75
Inverse Functions 76
Inverse Sine Function 78
Inverse Cosine Function 79
Inverse Tangent Function 80
Other Inverse Trigonometric Functions 87
Chapter 5 Basic Trigonometric Equations 93
Basic Sine Equation 94
Basic Cosine Equation 97
Basic Tangent Equation 100
Chapter 6 Trigonometry of Triangles 105
Solving Right Triangles 107
Solving Triangles: SSS and SAS Cases 113
Solving Triangles: SAA and SSA Cases 118
Areas of Triangles 131
Chapter 7 Trigonometric Identities and Equations 139
Fundamental Identities 140
Sum and Difference Identities 144
Double-Angle Identities 155
Half-Angle Identities 159
Product-to-Sum and Sum-to-Product Identities 162
Trigonometric Equations 165
Chapter 8 Vectors 171
Vector Operations 173
Vectors in a Rectangular Coordinate System 182
The Dot Product of Two Vectors 189
Chapter 9 Polar Coordinates and Complex Numbers 197
Polar Coordinates 198
Graphs of Polar Equations 199
Relationships Between Polar and Rectangular Coordinates 202
Complex Numbers 208
Polar Form of a Complex Number 210
Mulriplication and Division of Complex Numbers in Polar Form 212
De Moivre's Theorem and Powers of Complex Numbers in Polar Form 214
Complex Roots of Complex Numbers in Polar Form 216
Chapter 10 Additional Topics 221
Uniform Circular Motion 221
Simple Harmonic Motion 224
Review Questions 233
Glossary 243
Appendix: Theorems 247
Chapter 1 Geometric Prerequisites 247
Chapter 2 Trigonometric Numbers of Angles 248
Chapter 3 Trigonometric Functions 250
Chapter 4 Inverse Trigonometric Functions 251
Chapter 5 Basic Trigonometric Equations 251
Chapter 6 Trigonometry of Triangles 251
Chapter 7 Trigonometric Identities and Equations 252
Chapter 8 Vectors 255
Chapter 9 Polar Coordinates and Complex Numbers 256
Index 259
