Question

2sin² theta = sin theta for - 270° ≤ 0 ≤180°

Answer 1

θ = 0°

θ = 30°

θ = 150°

θ = 180°

Explanation:

2sin² θ = sin θ

Then

2sin² θ - sin θ = 0

Then

sin θ (2sin θ - 1) = 0

Then

sin θ = 0 or 2sin θ - 1 = 0

Then

sin θ = 0 or sin θ = 1/2

…………………………………………

We have sin θ = 0 and - 270° ≤ θ ≤180°

Then

θ = 0 or θ = π = 180°

On the other hand,

sin θ = 1/2 and - 270° ≤ θ ≤180°

Then

θ = π÷6 or θ = 5π÷6

π÷6 = 30° and 5π÷6 = 150°