Evaluate the following: ^ -1 ( 17 8 )

Question

Evaluate the following:
$\sin^{-1}\Big(\sin\frac{17\pi}{8}\Big)$

✓

Answer

We know
$\sin\big(\sin^{-1}\theta\big)=\theta$ if $-\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$
$\sin^{-1}\Big(\sin\frac{17\pi}{8}\Big)$
$=\sin^{-1}\Big(\sin\Big(2\pi+\frac{\pi}{8}\Big)\Big)$
$=\sin^{-1}\Big(\sin\Big(\frac{\pi}{8}\Big)\Big)$
$=\frac{\pi}{8}$

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