Find the value of the trigonometric function tan19π/3
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 $180^{\circ}$.

$\therefore \tan \frac{19 \pi}{3}=\tan 6 \frac{1}{3} \pi=\tan \left(6 \pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}=\tan 60^{\circ}=\sqrt{3}$

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