Question

If the value of expression ${\sin }^{-1}\left(\sin 2013^{\circ }\right)+{\cos }^{-1}(\cos$ $2013^{\circ })+{\tan }^{-1}\left(\tan 2013^{\circ }\right)$ is equal to $\left(k^{\circ }\right)$ where $k\in N$ then find the value of $\sqrt{\frac{k}{3}}$.

Answer 1

Answer: 7

${\sin }^{-1}\left(\sin 2013^{\circ }\right)+{\cos }^{-1}\left(\cos 2013^{\circ }\right)+{\tan }^{-1}\left(\tan 2013^{\circ }\right)$
$=-{\sin }^{-1}\sin 33^{\circ }+\pi -{\cos }^{-1}\cos 33^{\circ }+{\tan }^{-1}\tan 33^{\circ }$
$=\pi -33^{\circ }=147^{\circ }=k^{\circ }$
$\therefore$ The value of $\sqrt{\frac{k}{3}}=7$