How do you find the value of cot ((5pi/3) using the double angle or half angle identity?

Nov 11, 2016

$- \frac{\sqrt{3}}{3}$

Explanation:

Trig table and unit circle -->
$\cot \left(\frac{5 \pi}{3}\right) = \frac{1}{\tan} \left(\frac{5 \pi}{3}\right)$
Find $\tan \left(\frac{5 \pi}{3}\right)$
$\tan \left(\frac{5 \pi}{3}\right) = \tan \left(\frac{2 \pi}{3} + \pi\right) = \tan \left(\frac{2 \pi}{3}\right) = - \sqrt{3}$
There for:
$\cot \left(\frac{5 \pi}{3}\right) = - \frac{1}{\sqrt{3}} = - \frac{\sqrt{3}}{3}$