Question

Write the principal value of ${\cos }^{-1}\left[\cos \left(680\right)\right]$

Answer 1

${\cos }^{-1}\cos \left(680°\right)$

$\Rightarrow {\cos }^{-1}\left(\cos (720°-40°)\right)$

$\therefore {\cos }^{-1}\left(\cos \left(40°\right)\right)$ ($\because 720°=4\pi$ radian)

$\Rightarrow$Principal value$=40°$