From Förberedande kurs i matematik 1

If we use the unit circle and mark on the angle \displaystyle \pi, we see immediately that \displaystyle \cos \pi = -1 and \displaystyle \sin \pi = 0\,.

Thus,

\displaystyle \tan \pi =\frac{\sin \pi }{\cos \pi }=\frac{0}{-1}=0\,\textrm{.}