Solve over the interval 0 to 360

Question

 

2 sin ² theta + 3 cos theta = 3

Answer 1

2sin²θ + 3cosθ - 3 = 0

 

2(1 - cos²θ) + 3cosθ - 3 = 0

 

-2cos²θ + 3cosθ - 1 = 0

 

Divide both sides by -1:  2cos²θ - 3cosθ + 1 = 0

 

(2cosθ - 1)(cosθ - 1) = 0

 

cosθ = 1/2 or cosθ = 1

 

If cosθ = 1/2, then θ = 60° or 300°

 

If cosθ = 1, then θ = 0° or 360°