Evaluate the following: ^ -1 ( 13 7 ) - Vidyadip

Question

Evaluate the following:
$\sin^{-1}\Big(\sin\frac{13\pi}{7}\Big)$

✓

Answer

We know
$\sin\big(\sin^{-1}\theta\big)=\theta$ if $-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$
We have
$\sin^{-1}\Big(\sin\frac{13\pi}{7}\Big)=\sin^{-1}\Big\{\sin\Big(2\pi-\frac{\pi}{7}\Big)\Big\}$
$=\sin^{-1}\Big(\sin-\frac{\pi}{7}\Big)$
$=-\frac{\pi}{7}$

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