solve for theta in the interval 0 to 360

Question

2 sin² theta + 3 cos theta = 3 

Answer 1

2sin²θ+3cosθ=3

sin²+cos²=1

sin²=1-cos²

2(1-cos²θ)+3cosθ=3

2-2cos²θ+3cosθ-3=0

-2cos²θ+3cosθ-1=0

2cos²θ-3cosθ+1=0

(2cosθ-1)(cosθ-1)=0

2cosθ-1=0

2cosθ=1

cosθ=1/2

θ=60º (1st Q)

θ=360-60=300º (4th Q)

cosθ-1=0

cosθ=1

θ=0º