Use the given information to find the exact value of each of the following. a. s

Question

Use the given information to find the exact value of each of the following. a. sin 20 b. cos 20 c. tan 20 sin = 15.0 lies in quadrant II a. sin 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.) 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.) c, tan 2 = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Explanation / Answer

sin = 9/19 = Perp/Hyp

Base = sqrt[19^2 – 9^2] = sqrt(280)

cos = Base/Hyp = sqrt(280)/19

tan = Perp/Base = 9/sqrt(280)

a) sin2 = 2*sin*cos = 2*(9/19)*(sqrt(280)/19) = 18*sqrt(280)/361

b) cos2 = 2cos2 – 1 = 2(280)/361 - 1 = 199/361

c) tan2 = sin2/cos2 = 18*sqrt(280)/199

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