Find all solutions of in the interval .

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

Problem

Find all solutions of

\sin 2x = \dfrac{\sqrt{3}}{2}

in the interval

0 \le x < 2\pi

. (a)

\left\{\dfrac{\pi}{6},\;\dfrac{2\pi}{3},\;\dfrac{7\pi}{6},\;\dfrac{5\pi}{3}\right\}

(b)

\left\{\dfrac{\pi}{12},\;\dfrac{7\pi}{12},\;\dfrac{13\pi}{12},\;\dfrac{19\pi}{12}\right\}

(c)

\left\{\dfrac{\pi}{6},\;\dfrac{\pi}{3},\;\dfrac{7\pi}{6},\;\dfrac{4\pi}{3}\right\}

(d)

\left\{\dfrac{\pi}{6},\;\dfrac{5\pi}{6},\;\dfrac{7\pi}{6},\;\dfrac{11\pi}{6}\right\}