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

Question

sin 𝜃/2 + cos 𝜃 = 0

Answer 1

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

θ/2 = 90° or θ = 180°; or θ/2 = 210°, θ = 420° (outside of given interval)

So, answer is θ = 180°