\(cos^{-1}[cos(-680^o)]\)\(=cos^{-1}[cos(680^o)]\) \([\because cos(-\theta)=cos\,\theta]\)
\(=cos^{-1}[cos\,(720^o-40^o)]\)
\(=cos^{-1}[cos\,(4\pi-40^o)]\)\(=cos^{-1}(cos\,40^o)\)
\(=40^o\) or \(\frac{2\pi}9\) \([\because40^o=\frac{2\pi}9\in/0,\pi/]\)