Question

Evaluate Cos^-1(sin 330 degree)

Answer 1

$330^\circ\equiv-30^\circ\mod360^\circ$

so

$\sin330^\circ=\sin(-30^\circ)=-\sin30^\circ=-\dfrac12$

Finally,

$\cos^{-1}\left(-\dfrac12\right)=\dfrac{2\pi}3\text{ rad}=120^\circ$