Having issue with tan(7pi/6) converting degrees then to radical

Question

I'm trying to work out the following problem:

tan 7pi / 6

I first converted radians to degrees and got 210

tan(210 degrees) = 0.577350

How do I convert this to a radical? I'm having a hard time doing this.

Answer 1

$\tan$ is a periodic function with period $\pi$, then $$\tan \left(\frac{7\pi}{6}\right)=\tan \frac{\pi}{6}=\color{blue}{\frac{1}{\sqrt{3}}}$$