$\cos^{-1}\left(\cos frac{7\pi}{6} ight)$ equals

Question

$\cos^{-1}\left(\cos	frac{7\pi}{6}ight)$ equals

Accepted Answer

D. $	frac{5\pi}{6}$

$\cos^{-1}$ has range $[0, \pi]$, but $	frac{7\pi}{6} > \pi$. Reflect about the x-axis: $\cos	frac{7\pi}{6} = \cos\left(2\pi - 	frac{7\pi}{6}ight) = \cos	frac{5\pi}{6} = -	frac{\sqrt{3}}{2}$, and $	frac{5\pi}{6} \in [0,\pi]$. So the inverse returns $	frac{5\pi}{6}$.

Answer

$	frac{7\pi}{6}$

Answer

$-	frac{\pi}{6}$

Answer

$	frac{\pi}{6}$

$\cos^{-1}\left(\cos\tfrac{7\pi}{6}\right)$ equals