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Trigonometric Ratios Contents IIntroduction to Trigonometric Ratios UUnit Circle AAdjacent, opposite side and hypotenuse of a right angle triangle. TThree types trigonometric ratios CConclusion

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

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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

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

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Adjacent side Opposite side hypotenuse

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Adjacent side Opposite side

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

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

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

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

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

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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

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

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

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

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

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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

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

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

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

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

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Conclusion Make Sure that the triangle is right-angled

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END

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EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5.

EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5.

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