# How do you evaluate cos(sin^-1(1/2))?

$\cos \left({\sin}^{- 1} \left(\frac{1}{2}\right)\right) = \cos \left({\cos}^{- 1} \sqrt{1 - {\left(\frac{1}{2}\right)}^{2}}\right) = \sqrt{1 - {\left(\frac{1}{2}\right)}^{2}} = \frac{\sqrt{3}}{2.}$
Use ${\cos}^{- 1} x = {\sin}^{- 1} \left(\pm \sqrt{1 - {x}^{2}}\right)$.