Solve for the angle

Question

Solve for the angle θ where 0≤ θ ≤ 2∏

sin^2 θ = 1/4

θ =

Answer 1

sin²θ = 1/4 and we are looking for solutions on [0,2π]

Taking the square root of both sides (being careful not to forget the ± on the left) gives us

sinθ = ±1/2

Our reference angle (in the first quadrant) is π/6 since sin(π/6) = 1/2

the corresponding angles, and values of sinθ in the other three quadrants are

5π/6, sin(5π/6) = 1/2

7π/6, sin(7π/6) = –1/2

11π/6, sin(11π/6) = –1/2

Solutions (in increasing order)

π/6, 5π/6, 7π/6, 11π/6

Answer 2

sin²θ = 1/4

sinθ = 1/2 or -1/2

sinθ = 1/2 when θ = π/6, 5π/6

sinθ = -1/2 when θ = 7π/6, 11π/6