Question

Find the value of tan 19π/3​

Answer 1

Required Answer:-

Given to find:

• Value of tan(19π/3)

Solution:

Given,

$\rm \tan \bigg( \dfrac{19\pi}{3} \bigg)$

$\rm = \tan \bigg( \dfrac{18\pi + \pi}{3} \bigg)$

$\rm = \tan \bigg( \dfrac{18\pi }{3} + \dfrac{\pi}{3} \bigg)$

$\rm = \tan \bigg(6\pi + \dfrac{\pi}{3} \bigg)$

As we know that,

$\rm \mapsto \tan (x \pm k\pi) = \tan(x) , x \in \Z$

So,

$\rm \tan \bigg(6\pi + \dfrac{\pi}{3} \bigg)$

$\rm = \tan \bigg( \dfrac{\pi}{3} \bigg)$

Value of tan(π/3) is √3. So,

$\rm = \sqrt{3}$

Hence,

$\rm \mapsto \tan \bigg( \dfrac{19\pi}{3} \bigg) = \sqrt{3}$

Answer:

$\rm \mapsto \tan \bigg( \dfrac{19\pi}{3} \bigg) = \sqrt{3}$