asymptote of an arctangent

Given the function $y={\tan }^{-1}(x)$,

we see that it has two asymptotes, namely $\frac{\pi }{2}$ and $-(\frac{\pi }{2})$. This specific example of an asymptote was mentioned in an episode of the comedy TV show The Big Bang Theory, in which the mathematician Sheldon Eppes tries to explain his inability to reach the top of a rock wall, getting stuck at the same height each time. According to the Mathematica manual, the results of ArcTan for real $z$ ”are always in the range $-\pi /2$ to $\pi /2$.

Title	asymptote of an arctangent
Canonical name	AsymptoteOfAnArctangent
Date of creation	2013-03-22 18:51:01
Last modified on	2013-03-22 18:51:01
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Example
Classification	msc 51N99
Synonym	asymptote of an inverse tangent