Question:
The value of $\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)$ is
(a) $\frac{3 \pi}{5}$
(b) $-\frac{\pi}{10}$
(c) $\frac{\pi}{10}$
(d) $\frac{7 \pi}{5}$
Solution:
(b) $-\frac{\pi}{10}$
$\sin ^{-1}\left(\cos \frac{33 \pi}{5}\right)=\sin ^{-1}\left\{\cos \left(6 \pi+\frac{3 \pi}{5}\right)\right\}$
$=\sin ^{-1}\left\{\cos \left(\frac{3 \pi}{5}\right)\right\}$
$=\sin ^{-1}\left\{\sin \left(\frac{\pi}{2}-\frac{3 \pi}{5}\right)\right\}$
$=\frac{\pi}{2}-\frac{3 \pi}{5}$
$=-\frac{\pi}{10}$
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