Question

Find the value of $\sin \left[{\cos }^{-1}\left(\frac{-1}{2}\right)\right]$

Answer 1

$\sin \left[{\cos }^{-1}\left(\frac{-1}{2}\right)\right]$

$=\sin \left({\cos }^{-1}\left(\frac{-1}{2}\right)\right)$

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

$=\sin (\pi -\frac{\pi }{3})$

$=\sin \frac{\pi }{3}$

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