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Add hypotenuse, the three proportions, Pythagorean Thm. and Converse(obtuse, acute), multiply fractions vs. proportions, 45-45-90 and 30-60-90 formulas, Pythagorean triple, sin, cos, tangent to vocab list

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Geometry 8.6 The Sine and Cosine Ratios

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Sine ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Sine of

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Cosine ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Cosine of

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Easily remember all 3 trig ratios! SS o h CC a h TT o a sin opposite adjacent cos tan hypotenuse

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45 B 24 51 A A 15 12 9 B B 5 10 A 6 AB I. Express Sin A, Sin B, Cos A and Cos B as ratios. 1.2. 3.4.

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1) Express Sin A, Sin B, Cos A, and Cos B as ratios. 24 51 45 B A O A H O A

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Answers 2) sin A = 3/5, sin B = 4/5, cos A = 4/5, cos B = 3/5 3) sin A = 1/2, sin B =, cos A =, cos B = 3/5 4) All ratios are

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Exercises 13. Find the value of x and y to the nearest tenth. y x 52 o 34 (34).7880 ≈ x (34).6157 ≈ y O A H

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16 x y 43 y 34 52 x 6 47 x x y y xx 75 44 60 37 nn nn x 13 n 5 17. II. Find the value of x and y to the nearest tenth. 13.14. 15.16. 18.

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Exercises 15. Find the value of x and y to the nearest tenth. x x 6 47 o y sin 47 = 6 x.7314 ≈ 6 x x(.7314) ≈ 6 x ≈ 6.7314 x ≈ 8.2 a tan 47 = 6 a 1.0724 ≈ 6 a a(1.0724) ≈ 6 a ≈ 6 1.0724 a ≈ 5.6 y ≈ 11.2 O A H

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Exercises 17. Find n to the nearest degree. 60 37 nono H A cos n = 37 60 cos n ≈.6166 n ≈ 52 o

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HW 14. x ≈ 11.7, y ≈ 10.9 16. x ≈ 85, y ≈ 82.1 18. x = 12, n ≈ 67 o P. 313 CE (1-13)Odds P. 314 (1-17) Odds

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