Question

Find the value of ${\cos }^{-1}\left(\cos 13\right)$

Answer 1

${\cos }^{-1}\left(\cos 13\right)\in [0,\pi ]$

and we know ,

$\cos (\theta +2\pi )=\cos (2\pi -\theta )=\cos (\theta -2\pi )=\cos \theta$

$\therefore {\cos }^{-1}\left(\cos 13\right)={\cos }^{-1}\left(\cos \right(13-4\pi \left)\right)$

$=13-4\pi$