Question

Evaluate:
${\sin }^{-1}\left(\sin \frac{5\pi }{6}\right)$

Answer 1

${\sin }^{-1}\left(\sin \frac{5\pi }{6}\right)$

$={\sin }^{-1}\left(\sin (\pi -\frac{\pi }{6})\right)$

$={\sin }^{-1}\left(\sin \frac{\pi }{6}\right)$

$={\sin }^{-1}\left(\frac{1}{2}\right)$

Let ${\sin }^{-1}\left(\frac{1}{2}\right)=y$

$\Rightarrow \sin y=\frac{1}{2}$

$\Rightarrow \sin y=\sin \frac{\pi }{6}$ since $\sin \frac{\pi }{6}=\frac{1}{2}$

$\therefore y=\frac{\pi }{6}$