# How do you find the exact value of arcsin(sin((2pi)/3))?

Mar 2, 2017

$\arcsin \left(\sin \left(\frac{2 \pi}{3}\right)\right) = \frac{2 \pi}{3}$

#### Explanation:

By definition if $\sin A = x$, $\arcsin x = A$,

and substituting $x$ for $\sin A$ in $\arcsin x = A$

$\arcsin \left(\sin A\right) = A$ and hence

$\arcsin \left(\sin \left(\frac{2 \pi}{3}\right)\right) = \frac{2 \pi}{3}$