tan computes the tangent in radians for each element of x.

The tangent function is defined as:

$$\tan(x) = \frac{\sin(x)}{\cos(x)} = \frac{e^{ix} - e^{-ix}}{i(e^{ix} + e^{-ix})}$$

It has vertical asymptotes at

$$x = \frac{\pi}{2} + n\pi$$

for integer n.