Question

find the value of tan 19 pi by 3

Answer 1

Answer:

Step-by-step explanation:

Hope it helps

Answer 2

$\text { Value of } \tan \left(\frac{19 \pi}{3}\right) \text { is } \sqrt{3}$

Solution:

$\text{ Need to calculate value of } \tan \left(\frac{19 \pi}{3}\right)\\\\\text{ First we need to simplify } \frac{19 \pi}{3}$

$\frac{19 \pi}{3}=\frac{18 \pi}{3}+\frac{\pi}{3}=6 \pi+\frac{\pi}{3}=2 \times 3 \times \pi+\frac{\pi}{3}$

$\text { As } \tan (2 \times \mathrm{n} \times \pi+x)=\tan (x)$

$\begin{aligned}&\Rightarrow \tan \left(\frac{19 \pi}{3}\right)=\tan \left(2 \times 3 \times \pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}\\\\&\tan \frac{\pi}{3}=\tan 60=\sqrt{3}\end{aligned}$

[ we know that value of tan 60 = $\sqrt{3}$ ]

$\text { Hence value of } \tan \left(\frac{19 \pi}{3}\right) \text { is } \sqrt{3}$

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