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

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  1. Subject Mathematics (F.2)

  2. PROJECT TITLE Trigonometric Ratios

  3. Target Audience F.2 Students

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

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

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

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

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

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

  10. Opposite side hypotenuse Adjacent side

  11. hypotenuse Adjacent side Opposite side

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

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

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

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

  16. 4 7 Exercise 1 In the figure, find sin  Opposite Side Sin = hypotenuses 4 = 7  = 34.85 (corr to 2 d.p.)

  17. 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.)

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

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

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

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

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

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

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

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

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

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

  28. END

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