Question

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

Answer 1

⁡ $\tan \frac{19\pi }{3}=\tan \frac{18\pi +\pi }{3}$
$=\tan (6\pi +\frac{\pi }{3})$
$=\tan \left(3\right(2\pi )+\frac{\pi }{3})$

Values of $\tan x$ repeat after an interval of $\pi$,
hence ignoring $6\pi$.

$\therefore \tan \frac{19\pi }{3}=\tan \frac{\pi }{3}=\sqrt{3}$