Question

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

• A. $\frac{2\pi }{9}$
• B. $\frac{-2\pi }{9}$
• C. $\frac{34\pi }{9}$
• D. $\frac{\pi }{9}$

Answer 1

The correct option is A $\frac{2\pi }{9}$

${\cos }^{-1}\left(\cos \left({680}^{\circ }\right)\right)={\cos }^{-1}\left[\cos ({720}^{\circ }-{40}^{\circ })\right]={\cos }^{-1}\left[\cos \left({40}^{\circ }\right)\right]={40}^{\circ }(\because {\cos }^{-1}(\cos x)=x,x\in [0,\pi \left]\right)=\frac{2\pi }{9}$