Find all solutions in the interval 0° ≤ 𝜃 < 360°. If rounding is necessary, round to the nearest tenth of a degree.

Question

2 sin 𝜃 − csc 𝜃 = 1

Answer 1

2/sinθ - 1/sinθ = 1; 2sin²θ - sinθ - 1 = 0; (sinθ - 1)(2sinθ + 1) = 0; sinθ = 1 or sinθ = - 1/2;

θ = 90°; θ = 210°, θ = 330

Answer 2

2sinx - cscx = 1

2sinx - 1/sinx = 1

2sinx^2 - 1 = sinx

2sinx^2 - sinx - 1 = 0

(2sinx +1(sinx - 1) = 0

2sinx + 1 = 0 or sinx - 1 = 0

sinx = -1/2 or 1

x = 90, 210, 330