Question

Using the until circle, what is the exact value of tan 2pi/3

Answer 1

Tan 2 pi/3= (sin2pi/3)/(cos2pi/3)= (sqrt 3)/2 dividend by (-1/2)= - sqrt 3

Answer 2

Answer:

The exact value for the expression $\tan (\dfrac{2\pi}{3})$ is:

                      $\tan (\dfrac{2\pi}{3})=-\sqrt{3}$

Step-by-step explanation:

We are asked to find the exact value of the given trigonometric expression.

The expression is given as:

           $\tan (\dfrac{2\pi}{3})$

This could also be written as follows:

              $\tan (\dfrac{2\pi}{3})=\tan (\pi-\dfrac{\pi}{3})$

Now, we know that:

$\tan (\pi-\dfrac{\pi}{3})=-\tan (\dfrac{\pi}{3})$

Also, we have:

$\tan (\dfrac{\pi}{3})=\sqrt{3}$

Hence, we finally have:

              $\tan (\dfrac{2\pi}{3})=-\sqrt{3}$