Question:
Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$
Solution:
It is known that the values of $\tan x$ repeat after an interval of $\pi$ or $180^{\circ}$.
$\therefore \tan \frac{19 \pi}{3}=\tan 6 \frac{1}{3} \pi=\tan \left(6 \pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}=\tan 60^{\circ}=\sqrt{3}$