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  4. Given that sin -1( sin (3 π/4))=(2 π/ k ), then k =

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Q. Given that $\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)=\frac{2 \pi}{ k }$, then $k =$

Inverse Trigonometric Functions

Solution:

$\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)=\sin ^{-1}\left\{\sin \left(\pi-\frac{\pi}{4}\right)\right\}$
$=\sin ^{-1}\left\{\sin \left(\frac{\pi}{4}\right)\right\}=\sin ^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4}=\frac{2 \pi}{ k } $
$ \therefore k =8$