# What does arcsin(cos ((-pi)/3))  equal?

Feb 11, 2016

$\cos \left(- \frac{\pi}{3}\right) = \cos \left(\frac{\pi}{3}\right)$ because cosinus is even

watch your trigonometric circle you get

$\cos \left(\frac{\pi}{3}\right) = \frac{1}{2}$
you search a number $x$ such as

$\arcsin \left(\frac{1}{2}\right) = x$

$\frac{1}{2} = \sin \left(x\right)$

watch your circle again you get

${x}_{1} = \frac{\pi}{6} + 2 k \pi$ where $k \in \mathbb{Z}$

${x}_{2} = \pi - \frac{\pi}{6} + 2 k \pi$ where $k \in \mathbb{Z}$