Question

which of the following is equivalent to tan(5pi/6)

Answer 1

Step-by-step explanation:

We need to find the value of $\tan(\dfrac{5\pi}{6})$. We can write it as :

$\tan(\dfrac{5\pi}{6})=\tan(\pi -\dfrac{\pi}{6})$

We know that $(\pi -\theta)$ comes in second quadrant. The value of tan is negative. Also, $(\pi -\theta)$ do not change. So,

$\tan(\pi -\dfrac{\pi}{6})=\tan(\dfrac{\pi}{6})=\tan30=\dfrac{1}{\sqrt 3}$

So, the value of $\tan(\dfrac{5\pi}{6})$ is $\dfrac{1}{\sqrt 3}$.

Answer 2

We have find the value of  $tan\frac{5\pi }{6}$.

The given function lies in 2nd quadrant.

In the 2nd quadrant value of tanx is negative.

Then ,

      $= tan \frac{5\pi }{6} \\\\= tan ( \frac{(6-1)\pi }{6} )\\\\ = tan (\frac{6\pi - \pi }{6} )\\\\= tan (\frac{6\pi }{6} - \frac{\pi }{6} )\\\\= tan ( \pi -\frac{\pi }{6} )$

We know that ,  $tan(\pi - \theta )= -tan\theta$

So,

          $= tan ( \pi -\frac{\pi }{6} )$

          $= -tan (\frac{\pi }{6} )$

$tan \frac{5\pi }{6} = - \frac{1}{\sqrt{3} }$

The value of  $tan \frac{5\pi }{6}$  is  $\frac{-1}{\sqrt{3} }$ .

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