Solve the equation 6 6sin theta 4 cos2 theta What is the s

Solve the equation. 6 + 6sin theta = 4 cos^2 theta What is the solution in the interval 0 lessthanorequalto 9

Solution

6 + 6 sin theta=4 cos²theta

6 + 6 sin theta= 4-4 sin²theta

4 sin²theta + 6 sin theta +2=0

2 sin²theta + 3sin theta +1=0

2 sin²theta + 2 sin theta + 1 sin theta +1=0

(2 sin theta +1)(sin theta +1)=0

sin theta=-1/2 , sin theta=-1

theta=7pi/6, 11pi/6, 3pi/2