INTRODUCTION TO TRIGONOMETRY
CHAPTER 1. FUNDAMENTALS OF TRIGONOMETRY
A. THE UNIT CIRCLE
B. ANGLES AND DIRECTION
1. The Concept of Angle
2. Directed Angles
3. Directed Arcs
C. UNITS OF ANGLE MEASURE
1. Grad
2. Degree
3. Radian
4. Converting Units of Angle Measure
D. PRIMARY DIRECTED ANGLES
1. Coterminal Angles
2. Primary Directed Angles and Arcs
CHAPTER 2. RIGHT TRIANGLE TRIGONOMETRY
A. TRIGONOMETRIC RATIOS
1. Definition
2. Special Triangles and Ratios
B. TRIGONOMETRIC IDENTITIES
1. Basic Identities
a. Pythagorean identities
b. Tangent and cotangent identities
c. Reciprocal identities
2. Simplifying Trigonometric Expressions
3. Verifying Trigonometric Identities
4. Cofunctions
Calculating the Earth’s Circumference
CHAPTER 3. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS
A. TRIGONOMETRIC FUNCTIONS
1. The Sine Function
2. The Cosine Function
3. The Tangent Function
4. The Cotangent Function
5. The Secant and Cosecant Functions
B. CALCULATING TRIGONOMETRIC VALUES
1. Trigonometric Values of Quadrantal Angles
2. Using a Reference Angle
3. Calculating Ratios from a Given Ratio
4. Trigonometric Values of Other Angles
a. Using a trigonometric table
b. Using a calculator
CHAPTER 4. TRIGONOMETRIC THEOREMS AND FORMULAS
A. TRIGONOMETRIC THEOREMS
1. The Law of Cosines
2. The Law of Sines
3. Formulas for the Area of a Triangle
4. Further Theorems (Optional)
B. TRIGONOMETRIC FORMULAS
1. Sum and Difference Formulas
a. sin(x±y)
b. cos(x±y)
c. tan(x±y)
d. cot(x±y)
2. Double-Angle and Half-Angle Formulas
a. sin 2x
b. cos 2x
c. tan 2x
d. cot 2x
e. Half-angle formulas
3. Reduction Formulas
4. Sum to Product Formulas
a. sin a ± sin b
b. cos a ± cos b
c. tan a ± tan b
d. cot a ± cot b
5. Product to Sum Formulas
a. sin x ⋅ sin y
b. cos x ⋅ cos y
c. sin x ⋅ cos y
d. cos x ⋅ sin y
Triangulation and Surveying
CHAPTER 5. APPLIED TRIGONOMETRY