# How do you find the exact value of arctan [cos(-5pi/6)]?

Mar 14, 2016

${40.893}^{o}$ or $0.714$ radians

#### Explanation:

As $\cos \left(- 5 \frac{\pi}{6}\right) = - \frac{\sqrt{3}}{2} = - 0.866$,

$\arctan \left[\cos \left(- 5 \frac{\pi}{6}\right)\right]$ is an angle $\theta$ so that

$\tan \theta = - 0.866$ and

$\theta = \arctan \left(- 0.866\right) = {40.893}^{o}$ or $0.714$ radians