William D. Clark, PhD, is professor of mathematics at Stephen F. Austin State University.
Sandra Luna McCune, PhD, is a former Regents Professor who taught as a mathematics specialist at Stephen F. Austin State University.
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Introduction
CHAPTER 1 Angles and Their Measure
Definitions and Terminology
Complementary and Supplementary Angles
Coterminal Angles and Reference Angles
Radian Measure
CHAPTER 2 Concepts from Geometry
The Sum of a Triangle's Angles and the Triangle Inequality
The Pythagorean Theorem
CHAPTER 3 Right Triangle Trigonometry
Trigonometric Ratios of an Acute Angle in a Right Triangle
Trigonometric Ratios of Special Acute Angles
CHAPTER 4 General Right Triangles
Solving Right Triangles
Applications of Right Triangle Trigonometry
CHAPTER 5 Oblique Triangles
Law of Cosines (SAS or SSS)
Law of Sines (ASA or AAS)
Law of Sines Ambiguous Case (SSA)
Solving General Triangles
Area of a General Triangle Using Trigonometry
CHAPTER 6 Trigonometric Functions of Any Angle
Definitions of the Trigonometric Functions
Trigonometric Functions of Complementary Angles
The Unit Circle
Trigonometric Functions of Quadrantal Angles
Trigonometric Functions of Coterminal Angles
Trigonometric Functions of Negative Angles
Using Reference Angles to Find the Values of Trigonometric Functions
CHAPTER 7 Trigonometric Identities
Definition and Guidelines
The Reciprocal and Ratio Identities
The Pythagorean Identities
Sum and Difference Formulas for the Sine Function
Sum and Difference Formulas for the Cosine Function
Sum and Difference Formulas for the Tangent Function
Reduction Formulas
Double-Angle Identities
Half-Angle Identities
Sum-to-Product Identities
Product-to-Sum Identities
CHAPTER 8 Trigonometric Functions of Real Numbers
Definitions and Basic Concepts of Trigonometric Functions of Real Numbers
Periodic Functions
CHAPTER 9 Graphs of the Sine Function
The Graph of y = sin x
The Graph of y = A sin x
The Graph of y = A sin Bx
The Graph of y = A sin (Bx - C)
The Graph of y = A sin (Bx - C) + D
CHAPTER 10 Graphs of the Cosine Function
The Graph of y = cos x
The Graph of y = A cos (Bx - C) + D
CHAPTER 11 Graphs of the Tangent Function
The Graph of y = tan x
The Graph of y = A tan (Bx - C) + D
CHAPTER 12 Graphs of the Secant, Cosecant, and Cotangent Functions
The Graph of y = A sec (Bx - C) + D
The Graph of y = A csc (Bx - C) + D
The Graph of y = A cot (Bx - C) + D
CHAPTER 13 Inverse Trigonometric Functions
The Inverse Sine, Cosine, and Tangent Functions
The Inverse Secant, Cosecant, and Cotangent Functions
CHAPTER 14 Solving Trigonometric Equations
Basic Concepts of Trigonometric Equations
Solving for Exact Solutions to Trigonometric Equations
Solving for Approximate Solutions to Trigonometric Equations
CHAPTER 15 Trigonometric Form of a Complex Number
Definition of the Trigonometric Form of a Complex Number
The Product and Quotient of Trigonometric Forms of Complex Numbers
De Moivre's Theorem
Roots of Complex Numbers
CHAPTER 16 Polar Coordinates
Basic Concepts of Polar Coordinates
Converting Between Coordinate Systems
Graphing Equations in Polar Form
Glossary
APPENDIX A Calculator Instructions for Trigonometry Using the TI-84 Plus
General Usage
Setting the Calculator to Degree or Radian Mode
Overriding Radian or Degree Mode
Evaluating Trigonometric Functions
Determining Inverse Trigonometric Values
Graphing Polar Equations
APPENDIX B Trigonometric Identities
APPENDIX C The Complex Plane
Answer Key