Question

Find the value of $\tan \frac{19\pi }{3}$

Answer 1

It is known that the values of $\tan x$ repeat after an interval of $\pi$ or ${180}^{\circ }$
$\therefore \tan \frac{19\pi }{3}=\tan 6\frac{1}{3}\pi =\tan (6\pi +\frac{\pi }{3})$

$=\tan \frac{\pi }{3}$

$=\tan {60}^{\circ }$

$=\sqrt{3}$