# How do you find \sin(\sin^{-1}(\frac{1}{4})) ?

How do you find $\mathrm{sin}\left({\mathrm{sin}}^{-1}\left(\frac{1}{4}\right)\right)$ ?
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Eliza Norris
Recall that $\mathrm{sin}\left[\mathrm{arcsin}\left(x\right)\right]=x$ for x in the domain of $\mathrm{arcsin}\left(x\right)$
(The domain of $\mathrm{arcsin}\left(x\right)$ is: $-1\le x\le 1$)
Therefore $\mathrm{sin}\left[\mathrm{arcsin}\left(\frac{1}{4}\right)\right]=\frac{1}{4}$
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waijazar1
If:
$y=\mathrm{sin}x$
Then:
$\mathrm{arcsin}\left(y\right)=x$
Hence:
$\mathrm{arcsin}\left(\mathrm{sin}x\right)=x$
So:
$\mathrm{arcsin}\left(\mathrm{sin}\left(\frac{1}{4}\right)\right)=\frac{1}{4}$