# How do you evaluate tan((5pi)/3)?

##### 1 Answer
Apr 26, 2015

The intersection of the ray for $\frac{5 \pi}{3}$ with the unit circle is at the same place as the ray for $\left(- \frac{\pi}{3}\right)$

Again with reference to the unit circle that intersection point is at
$\left(x , y\right) = \left(\frac{1}{2} , - \frac{\sqrt{3}}{2}\right)$

So
$\tan \left(\frac{5 \pi}{3}\right) = - \sqrt{3}$