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Trigonometry
1 INTRODUCTION TO TRIGONOMETRY , 1
1.1 The Measurement of Angles , 1
1.2 Basic Trigonometrical Ratios , 3
1.3 The Reciprocal Trigonometrical Ratios of Acute Angles , 9
1.4 Relation Between Functions of the Same Angle , 12
1.5 The Determination of the Numerical Value of Trigonometrical
Ratios , 14
1.6 Projections , 15
Problems , 20.
2 THE TRIGONOMETRICAL RATIOS OF ANGLES GREATER THAN 90o , 26
3 PRACTICAL APPLICATION OF TRIGONOMETRY , 29
PROBLEMS , 45
4 APPLICATION OF TRIGONOMETRY TO THE AREA OF PLANE FIGURES , 59
4.1 The Area of a Triangle , 59
4.2 The Area of a Regular Polygon , 60
4.3 The Area of a Segment of a Circle , 63
Problems , 67
5 THE SINE AND COSINE RULE , 69
5.1 The Sine Rule , 69
5.2 The Cosine Rule , 75
Problems , 81.
6 THE SOLUTION OF TRIANGLE PROBLEMS , 84
6.1 The Solution of Scalene Triangle Problems , 84
6.2 Navigational Directional Bearings and Velocity , 93
6.3 Trigonometrical Problems in Three Dimensions , 97
Problems , 105.
7 IDENTITIES , 112
Problems , 115
8 COMPOUND ANGLES , 117
Problems , 127
9 THE GRAPHS OF TRIGONOMETRICAL FUNCTIONS , 130
9.1 The Sine and Cosine Curves , 130
9.2 Periodic Functions , 136
9.3 Angular Velocity, Periodic Time & Frequency , 142
9.4 Combination of Two Waves of the Same Period , 144
Problems , 147
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