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Why is -30 degrees not a solution for sintheta = - 1/2?
- Wayne DeguManLv 71 month ago
sinθ = -1/2
so, θ = sin⁻¹(-1/2)
Hence, θ = -30° + 360n° or (180 - (-30))° + 360n°...for n = 0, 1, 2,...
i.e. θ = -30° ± 360n° or 210° ± 360n°
so, θ = -30° is a possible solution
However, when solving trigonometric equations we get an infinite number of possible solutions as sinθ is continuous and periodic every 360°.
so, if we were asked to solve sinθ = -1/2 for a sspecified domain i.e. 0 ≤ θ ≤ 360° we would have:
θ = 210° and 330°
But for -360° ≤ θ ≤ 360° we would have:
θ = -150°, -30°, 210° and 330°
- ?Lv 71 month ago
It is a solution. Possible sources of thinking it isn't are using radians instead of degrees or being required to give solutions between 0 and 360
- BryceLv 71 month ago
Is there a domain given? -30° might not be in the given domain; otherwise, it would be a correct solution.