Solve for in the interval .

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Solve sin⁡(θ−π6)=12\sin\left(\theta - \dfrac{\pi}{6}\right) = \dfrac{1}{2} for θ\theta in the interval 0≤θ<2π0\le \theta < 2\pi. (a) {π6,  5π6}\left\{\dfrac{\pi}{6},\;\dfrac{5\pi}{6}\right\} (b) {π3,  π}\left\{\dfrac{\pi}{3},\;\pi\right\} (c) {0,  2π3}\left\{0,\;\dfrac{2\pi}{3}\right\} (d) {π3,  4π3}\left\{\dfrac{\pi}{3},\;\dfrac{4\pi}{3}\right\}

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