Question:
If $\cos x=-\frac{1}{2}$ and $0 (a) $x=\frac{\pi}{3}, \frac{4 \pi}{3}$ (b) $x=\frac{2 \pi}{3}, \frac{4 \pi}{3}$ (c) $x=\frac{2 \pi}{3}, \frac{7 \pi}{6}$ (d) $\theta=\frac{2 \pi}{3}, \frac{5 \pi}{3}$
Solution:
(b) $x=\frac{2 \pi}{3}, \frac{4 \pi}{3}$
Given equation:
$\cos x=-\frac{1}{2}$
$\Rightarrow \cos x=\cos \frac{2 \pi}{3}$
$\Rightarrow x=\frac{2 \pi}{2}$
Or,
$\cos x=\cos \frac{4 \pi}{3}$
$\Rightarrow x=\frac{4 \pi}{3}$
So, both $\frac{2 \pi}{3}$ and $\frac{4 \pi}{3}$ lie in $0