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The value of

Question:

The value of sin-1 cos 33π/5 is

(a) 3π/5

(b) -7π/5

(c) π/10

(d) -π/10

Solution:

(d) -π/10

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

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

$=\sin ^{-1}\left(\sin \left(-\frac{\pi}{10}\right)\right)$

$=-\frac{\pi}{10} \quad\left(\because \sin ^{-1}(\sin x)=x\right.$, for $\left.x \in\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\right)$

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