solve for theta in the interval 0 to 360

Question

2 sin² theta = 2 - 3 sin theta

Answer 1

2sin²θ + 3sinθ - 2 = 0

 

(2sinθ - 1)(sinθ + 2) = 0

 

sinθ = 1/2 or sinθ = -2

 

sinθ = -2 has no solution since -1 < sinθ < 1

 

If sinθ = 1/2, then θ = 30° or 150°