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Chapter 4 Trigonometric Functions 4

Ⅰ Trigonometric Functions of an Arbitrary Angle 4

4.1 Concept of Angle and Its Extension 4

4.2 Radian System 8

4.3 Trigonometric Functions of an Arbitrary Angle 14

Reading Material The Origin of Radian System 24

4.4 Basic Identities among Trigonometric Functions of the Same Angle 26

4.5 Induced Formulas of Sine and Cosine 30

Ⅱ Trigonometric Functions of Sum and Difference of Two Angles 36

4.6 Sine,Cosine and Tangent of Sum and Difference of Two Angles 36

4.7 Sine,Cosine and Tangent of Double Angle 45

Ⅲ Images and Properties of Trigonometric Functions 51

4.8 Images and Properties of Sine and Cosine Functions 51

4.9 Images of Function y=Asin（ωx＋？） 63

4.10 Images and Properties of Tangent Function 72

4.11 Evaluate an Angle from Given Value of a Trigonometric Function 76

Reading Material Addition of Sine Currents with Same Frequency,Frequency Unchanged 82

Summary and Review 84

Reference Exercises for Review Ⅳ 92

Chapter 5 Planar Vectors 100

Ⅰ Vectors and Their Operations 100

5.1 Vectors 100

5.2 Addition and Subtraction of Vectors 103

5.3 Product of a Real Number and a Vector 110

5.4 Coordinate Operations of Planar Vectors 115

5.5 Point with a Certain Ratio on a Segment 120

5.6 Inner Product and Its Operational Law of Planar Vectors 123

5.7 Coordinate Representation of Inner Product of Planar Vectors 127

5.8 Translation 129

Reading Material Three Types of Vectors 133

Ⅱ Solving a Skew Triangle 135

5.9 Sine Theorem,Cosine Theorem 135

5.10 Application Examples of Solving Skew Triangles 141

5.11 Practice Exercises 144

Reading Material How Did People Measure the Radius of the Earth in Early Time 148

5.12 Research Subject:Application of Vectors in Physics 149

Summary and Review 153

Reference Exercises for Review Ⅴ 159