Explanation

(d)
$\cos{\left( \frac{33\pi}{5} \right) = \cos{\left( 6\pi + \frac{3\pi}{5} \right) = \cos\frac{3\pi}{5}}}$
$= \sin{\left( \frac{\pi}{2} - \frac{3\pi}{5} \right) = \sin\left( - \frac{\pi}{10} \right)}$
$= \sin^{- 1}{\sin{\left( - \frac{\pi}{10} \right) = - \frac{\pi}{10}}}$