# How do you find the exact value of sin ( sin^-1 3/8)?

Sep 23, 2015

$\frac{3}{8}$

#### Explanation:

$S {\in}^{- 1}$ is the conventional notation for the inverse of the sin function.

The inverse of some function "undoes" the work of that function.

That is, application of the inverse of a function to the value taken by that function applied to some particular argument will return the original argument.

Similarly, application of some function to the value taken by the inverse of the function applied to some particular argument will return the original argument.

Hence $\sin \left({\sin}^{- 1} \left(x\right)\right) = x$

In the case of this particular question, $x = \frac{3}{8}$

So $\sin \left({\sin}^{- 1} \left(\frac{3}{8}\right)\right) = \frac{3}{8}$