Subject Mathematics (F.2)

PROJECT TITLE Trigonometric Ratios

Target Audience F.2 Students

How Slides are going to be used ? The Slide are going to be used during lesson

A computer with the following software installed System Requirement A computer with the following software installed Power Point 97/2000

Trigonometric Ratios Contents Introduction to Trigonometric Ratios Unit Circle Adjacent , opposite side and hypotenuse of a right angle triangle. Three types trigonometric ratios Conclusion

Introduction Trigonometric Ratios Trigonometry (三角幾何) means “Triangle” and “Measurement” In F.2 we concentrated on right angle triangles.

Unit Circle A Unit Circle Is a Circle With Radius Equals to 1 Unit.(We Always Choose Origin As Its centre) 1 units x Y

Adjacent , Opposite Side and Hypotenuse of a Right Angle Triangle.

 Opposite side hypotenuse Adjacent side

 hypotenuse Adjacent side Opposite side

Three Types Trigonometric Ratios There are 3 kinds of trigonometric ratios we will learn. sine ratio cosine ratio tangent ratio

Definition of Sine Ratio. Application of Sine Ratio. Sine Ratios Definition of Sine Ratio. Application of Sine Ratio.

Definition of Sine Ratio.  Opposite sides 1 If the hypotenuse equals to 1 Sin =

Definition of Sine Ratio.  Opposite side hypotenuses For any right-angled triangle Sin =

 Exercise 1 In the figure, find sin  4 Opposite Side Sin = 7 hypotenuses 4 = 7  = 34.85 (corr to 2 d.p.)

35° Exercise 2 In the figure, find y y Opposite Side Sin35 = hypotenuses 35° 11 y Sin35 = 11 y = 11 sin35 y = 6.31 (corr to 2.d.p.)

Cosine Ratios Definition of Cosine. Relation of Cosine to the sides of right angle triangle.

Definition of Cosine Ratio.  1 Adjacent Side If the hypotenuse equals to 1 Cos =

Definition of Cosine Ratio.  hypotenuses Adjacent Side For any right-angled triangle Cos =

 Exercise 3 3 In the figure, find cos  adjacent Side cos = 8 hypotenuses 3 = 8  = 67.98 (corr to 2 d.p.)

42° Exercise 4 In the figure, find x 6 Adjacent Side Cos 42 = hypotenuses x 6 Cos 42 = x 6 x = Cos 42 x = 8.07 (corr to 2.d.p.)

Tangent Ratios Definition of Tangent. Relation of Tangent to the sides of right angle triangle.

Definition of Tangent Ratio. Opposite Side  Adjacent Side For any right-angled triangle tan =

 Exercise 5 3 In the figure, find tan  Opposite side 5 tan = adjacent Side  3 = 5  = 78.69 (corr to 2 d.p.)

22 Exercise 6 In the figure, find z z Opposite side tan 22 = adjacent Side 5 5 tan 22 = z 5 z = tan 22 z = 12.38 (corr to 2 d.p.)

Make Sure that the triangle is right-angled Conclusion Make Sure that the triangle is right-angled

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