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

Inverse Trigonometric Functions

Solution:

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