6120 (4 complete) Use the given information to find the exact value of each of t

Question

6120 (4 complete) Use the given information to find the exact value of each of the following. a. sin 20 b. cos 20 c. tan 20 , lies in quadrant II 15 sin = a. sin 20 = (Simplify your answer Type an exact answer, using radicals as needed Use integers or fractions for any numbers in the expression. Ratinalize all lenoaminators) b cos 20= (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators) y numbers in the expression. Rationalize all denominators) C. tan 2 = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for an Enter your answer in each of the answer boxes.

Explanation / Answer

Given     sin = 4/15,     lies in quadrant II

cos = sqrt[1 – sin^2 ] = sqrt[1 – (16/225)] = sqrt(209/225)

a) sin2 = 2*sin*cos = 2*(4/15)* sqrt(209)/15 = (8/225)* sqrt(209) = 0.514

b) cos2 = sqrt[1 – sin^2 2] = sqrt[1 – 0.264] = 0.858

c) tan2 = sin2/cos2 = 0.514/0.858 = 0.6

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