Question

what is the exact value of tan  -13pi/6 and also the explanation

Answer 1

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

Answer 2

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