Question

Find the value of following function;

$co{s}^{-1}\left(cos\frac{13\pi }{6}\right)$

Answer 1

$co{s}^{-1}\left(cos\frac{13\pi }{6}\right)=co{s}^{-1}\left[cos(2\pi +\frac{\pi }{6})\right];where\frac{\pi }{6}ϵ[0,\pi ]$

[Hence, the] given angle does not lie in the principal interval i.e., $\left[0\pi \right]$, so we convert it such that it lies in $\left[0\pi \right]$.]
$co{s}^{-1}\left[cos\left(\frac{\pi }{6}\right)\right]=\frac{\pi }{6}$

$[\because cos(2\pi +\theta )=cos\theta ]$