Unit circle! XD Pi/6 is in the 30 degree family. What I do is multiply it by 180/pi to get it into degrees. Once you do this, the answer is -390

[latex]tan\left(-\frac{13\pi}{6}\right)=-tan\left(2\frac{1}{6}\pi\right)=-tan\left(2\pi+\frac{1}{6}\piright)=-tan\frac{1}{6}\pi=-\frac{\sqrt3}{3}[/latex]