Nataly Best

2022-01-23

How do you find $\mathrm{sin}\left({\mathrm{sin}}^{-1}\left(\frac{1}{4}\right)\right)$ ?

Eliza Norris

Beginner2022-01-24Added 15 answers

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$\mathrm{sin}\left[\mathrm{arcsin}\left(\frac{1}{4}\right)\right]=\frac{1}{4}$

(The domain of

Therefore

waijazar1

Beginner2022-01-25Added 13 answers

If:

$y=\mathrm{sin}x$

Then:

$\mathrm{arcsin}\left(y\right)=x$

Hence:

$\mathrm{arcsin}\left(\mathrm{sin}x\right)=x$

So:

$\mathrm{arcsin}\left(\mathrm{sin}\left(\frac{1}{4}\right)\right)=\frac{1}{4}$

Then:

Hence:

So:

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