Evaluate the following: ^ -1 ( 3) - Vidyadip

Question

Evaluate the following:
$\sin^{-1}(\sin3)$

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Answer

We know

$\sin\big(\sin^{-1}\theta\big)=\theta$ if $-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$

We have

$\sin^{-1}(\sin3)=\sin^{-1}\{\sin(\pi-3)\}=\pi-3$

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