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Trigonometric Ratios Contents IIntroduction to Trigonometric Ratios UUnit Circle AAdjacent, opposite side and hypotenuse of a right angle.

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Presentation on theme: "Trigonometric Ratios Contents IIntroduction to Trigonometric Ratios UUnit Circle AAdjacent, opposite side and hypotenuse of a right angle."— Presentation transcript:

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7 Trigonometric Ratios Contents IIntroduction to Trigonometric Ratios UUnit Circle AAdjacent, opposite side and hypotenuse of a right angle triangle. TThree types trigonometric ratios CConclusion

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

9 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

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

11 Adjacent side Opposite side  hypotenuse

12  Adjacent side Opposite side

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

14 Sine Ratios  Definition of Sine Ratio.  Application of Sine Ratio.

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

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

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

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

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

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

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

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

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

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

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

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

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

28 Conclusion Make Sure that the triangle is right-angled

29 END


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