The value of $cos^{-1}\left(cos (-680°)\right)$, is

$\frac{\pi}{9}$ $\frac{2\pi}{9}$ $\frac{4\pi}{9}$ $-\frac{\pi}{9}$

$\frac{2\pi}{9}$

$cos^{-1}\begin{Bmatrix}cos (-680°)\end{Bmatrix}=cos^{-1} (680°)$ $=cos^{-1}\begin{Bmatrix}cos\left(680×\frac{\pi}{180}\right)\end{Bmatrix}=cos^{-1}\left(cos\frac{34\pi}{9}\right)$ $=cos^{-1}\begin{Bmatrix}cos\left(4\pi -\frac{2\pi}{9}\right)\end{Bmatrix}=cos^{-1}\left(cos\frac{2\pi}{9}\right)=\frac{2\pi}{9}$