Solve for all in satisfying

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

Problem

Solve for all

\theta

0\le \theta<2\pi

satisfying

\cos 3\theta=-\dfrac{1}{2}

. Which of the following lists gives all the solutions? (a)

\theta=\dfrac{2\pi}{9},\,\dfrac{4\pi}{9},\,\dfrac{8\pi}{9},\,\dfrac{10\pi}{9},\,\dfrac{14\pi}{9}

(b)

\theta=\dfrac{\pi}{9},\,\dfrac{5\pi}{9},\,\dfrac{7\pi}{9},\,\dfrac{11\pi}{9},\,\dfrac{13\pi}{9},\,\dfrac{17\pi}{9}

(c)

\theta=\dfrac{2\pi}{9},\,\dfrac{4\pi}{9},\,\dfrac{8\pi}{9},\,\dfrac{10\pi}{9},\,\dfrac{14\pi}{9},\,\dfrac{16\pi}{9}

(d)

\theta=\dfrac{2\pi}{9},\,\dfrac{8\pi}{9},\,\dfrac{14\pi}{9}