Question

Find the domain of definition of the following function:
$y=\sqrt{3\sin x-1}$

Answer 1

$y=\sqrt{3\sin x-1},$

$3\sin x-1\ge 0,$

$\sin \ge \frac{1}{3}$

$\therefore$ $x\in [2n\pi +{\sin }^{-1}(\frac{1}{3}),(2n+1)\pi -{\sin }^{-1}(\frac{1}{3}\left)\right].$