# How do you simplify the expression sin(arccos(1/2))?

Jun 11, 2016

$\frac{\sqrt{3}}{2}$

#### Explanation:

$\arccos x \equiv {\cos}^{-} 1 x$
Given expression is
$\sin \left(\arccos \left(\frac{1}{2}\right)\right)$
$= \sin \left({\cos}^{-} 1 \left(\frac{1}{2}\right)\right)$
or $\sin \left({60}^{\circ}\right)$
or $\frac{\sqrt{3}}{2}$