Use the given information to find the exact value of each of

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.)

Solution

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