The solutions of in the interval are

MATHEMATICS · Single correct · ISC · Mathematics · Sets and Functions · Sets and Functions

Problem

The solutions of sin⁡2θ=32\sin 2\theta = \dfrac{\sqrt{3}}{2} in the interval 0≤θ<2π0 \leq \theta < 2\pi are (a) {π3,  2π3,  4π3,  5π3}\left\{\dfrac{\pi}{3},\; \dfrac{2\pi}{3},\; \dfrac{4\pi}{3},\; \dfrac{5\pi}{3}\right\} (b) {π4,  3π4,  5π4,  7π4}\left\{\dfrac{\pi}{4},\; \dfrac{3\pi}{4},\; \dfrac{5\pi}{4},\; \dfrac{7\pi}{4}\right\} (c) {π6,  π3,  7π6,  4π3}\left\{\dfrac{\pi}{6},\; \dfrac{\pi}{3},\; \dfrac{7\pi}{6},\; \dfrac{4\pi}{3}\right\} (d) {π6,  5π6,  7π6,  11π6}\left\{\dfrac{\pi}{6},\; \dfrac{5\pi}{6},\; \dfrac{7\pi}{6},\; \dfrac{11\pi}{6}\right\}

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