Find the value of $\sin^{-1} \left( \cos \frac{33\pi}{5} \right)$.

$-\frac{\pi}{10}$

The correct answer is Option (3) → $-\frac{\pi}{10}$ ##

$\sin^{-1} \left( \cos \frac{33\pi}{5} \right) = \sin^{-1} \left( \cos \left( 6\pi + \frac{3\pi}{5} \right) \right)$

$= \sin^{-1} \left( \cos \frac{3\pi}{5} \right)$

$= \frac{\pi}{2} - \cos^{-1} \left( \cos \frac{3\pi}{5} \right)$

$= \frac{\pi}{2} - \frac{3\pi}{5} = -\frac{\pi}{10}$