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  4. The value of sin -1( cos (19 π/6)) is equal to

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Q. The value of $\sin ^{-1}\left(\cos \frac{19 \pi}{6}\right)$ is equal to

Inverse Trigonometric Functions

Solution:

$ \cos \left(\frac{19 \pi}{6}\right)=\cos \left(\frac{7 \pi}{6}\right)=\sin \left(\frac{-\pi}{3}\right) $
$\cos \left(\frac{7 \pi}{6}\right)=\cos \left(\pi+\frac{\pi}{6}\right)-\cos \left(\frac{\pi}{6}\right)=\frac{-\sqrt{3}}{2} $
$\therefore \sin ^{-1}\left(\cos \frac{19 \pi}{6}\right)=\sin ^{-1}\left(\sin \left(\frac{-\pi}{3}\right)\right)=\frac{-\pi}{3}$