# How do you find the exact value of sin(arccos(1/2))?

$\sin \left(\arccos \left(\frac{1}{2}\right)\right) = \frac{\sqrt{3}}{2}$
As $\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$
$\arccos \left(\frac{1}{2}\right) = \frac{\pi}{3}$
Hence, $\sin \left(\arccos \left(\frac{1}{2}\right)\right) = \sin \left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$