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 sin 2 theta cos 2 thetas can 2 theta sin theta = 9/11 theta lies in quadrant sin 2 theta = Simplify your answer type an exact answer, using radicals as needed simplify your answer Type an exact answer. using radicals as needed Simplify your answer Type an exact answer, using radicals as needed.

Solution

sin theta=9/11

here opposite=9

hypetenuse=11

adjacent=sqrt(11²-9²) = sqrt 40= 2sqrt10

cos theta=adjacent/hypotenuse= -2sqrt10/11

theta is in second quadrant and in second quadrant cosine is negative

a.sin 2theta

sin 2theta=2 sin theta cos theta

=2(9/11)(-2 sqrt10/11) = -36sqrt 10/121

b. cos 2 theta =2 cos²theta -1 = 2 (- 2 sqrt 10/11)²-1 = -41/121

c. tan 2 theta= sin 2 theta/ cos 2 theta = 36 sqrt10/41