INTRO TO TRIGONOMETRY
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INTRO TO TRIGONOMETRY
Preparing book pages
1
Entries
84
1. Fundamentals of Trigonometry
Theory
Page 10
1A. The Unit Circle
Theory
Page 10
1B. Angles and Direction
Theory
Page 12
1B1. The Concept of Angle
Theory
Page 12
1B2. Directed Angles
Theory
Page 12
1B3. Directed Arcs
Theory
Page 13
1C. Units of Angle Measure
Theory
Page 14
1C1. Grad
Theory
Page 14
1C2. Degree
Theory
Page 15
1C3. Radian
Theory
Page 17
1C4. Converting Units of Angle Measure
Theory
Page 19
1D. Primary Directed Angles
Theory
Page 21
1D1. Coterminal Angles
Theory
Page 21
1D2. Primary Directed Angles and Arcs
Theory
Page 23
Exercises 1
Problem
Page 27
2. Right Triangle Trigonometry
Theory
Page 29
2A. Trigonometric Ratios
Theory
Page 29
2A1. Definition
Theory
Page 29
2A2. Special Triangles and Ratios
Theory
Page 32
2B. Trigonometric Identities
Theory
Page 34
2B1. Basic Identities
Theory
Page 34
2B1a. Pythagorean Identities
Theory
Page 34
2B1b. Tangent and Cotangent Identities
Theory
Page 35
2B1c. Reciprocal Identities
Theory
Page 36
2B2. Simplifying Trigonometric Expressions
Theory
Page 38
2B3. Verifying Trigonometric Identities
Theory
Page 41
2B4. Cofunctions
Theory
Page 44
Calculating the Earth's Circumference
Theory
Page 46
Exercises 2
Problem
Page 47
3. Trigonometric Functions of Real Numbers
Theory
Page 49
3A. Trigonometric Functions
Theory
Page 49
3A1. The Sine Function
Theory
Page 49
3A2. The Cosine Function
Theory
Page 51
3A3. The Tangent Function
Theory
Page 53
3A4. The Cotangent Function
Theory
Page 55
3A5. The Secant and Cosecant Functions
Theory
Page 57
3B. Calculating Trigonometric Values
Theory
Page 60
3B1. Trigonometric Values of Quadrantal Angles
Theory
Page 60
3B2. Using a Reference Angle
Theory
Page 62
3B3. Calculating Ratios from a Given Ratio
Theory
Page 66
3B4. Trigonometric Values of Other Angles
Theory
Page 68
3B4a. Using a Trigonometric Table
Theory
Page 68
3B4b. Using a Calculator
Theory
Page 71
Exercises 3
Problem
Page 73
4. Trigonometric Theorems and Formulas
Theory
Page 76
4A. Trigonometric Theorems
Theory
Page 76
4A1. The Law of Cosines
Theory
Page 76
4A2. The Law of Sines
Theory
Page 79
4A3. Formulas for the Area of a Triangle
Theory
Page 82
4A4. Further Theorems (Optional)
Theory
Page 86
4B. Trigonometric Formulas
Theory
Page 88
4B1. Sum and Difference Formulas
Theory
Page 88
4B1a. sin(x ± y)
Theory
Page 88
4B1b. cos(x ± y)
Theory
Page 89
4B1c. tan(x ± y)
Theory
Page 90
4B1d. cot(x ± y)
Theory
Page 92
4B2. Double-Angle and Half-Angle Formulas
Theory
Page 93
4B2a. sin 2x
Theory
Page 93
4B2b. cos 2x
Theory
Page 95
4B2c. tan 2x
Theory
Page 96
4B2d. cot 2x
Theory
Page 96
4B2e. Half-Angle Formulas
Theory
Page 97
4B3. Reduction Formulas
Theory
Page 101
4B4. Sum to Product Formulas
Theory
Page 106
4B4a. sin a ± sin b
Theory
Page 106
4B4b. cos a ± cos b
Theory
Page 108
4B4c. tan a ± tan b
Theory
Page 110
4B4d. cot a ± cot b
Theory
Page 111
4B5. Product to Sum Formulas
Theory
Page 112
4B5a. sin x · sin y
Theory
Page 112
4B5b. cos x · cos y
Theory
Page 113
4B5c. sin x · cos y
Theory
Page 114
4B5d. cos x · sin y
Theory
Page 114
Triangulation and Surveying
Theory
Page 116
Exercises 4
Problem
Page 117
5. Applied Trigonometry
Theory
Page 122
Exercises 5
Problem
Page 126
Chapter Summary
Theory
Page 130
Concept Check
Test
Page 133
Chapter Review Test 1
Test
Page 134
Chapter Review Test 2
Test
Page 136
Chapter Review Test 3
Test
Page 138
Answers
Answer
Page 140
Glossary
Other
Page 143
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