User:LucasVB/Square sine and cosine functions

The square sine along with the common sine

The square sine and square cosine functions are akin to their trigonometric counterparts, but instead of defining an unit circle, they define a square of "radius" 1 (that is, side 2). I'm not sure if such functions are already properly defined in the mathematical community, but I never heard of them. I doubt I'm the first to toy with this concept, though.

The square sine ("sinski") can be written as:

${\mbox{sinsq}}(x)=\tan(x)\operatorname {sgn}(\cos(x))((\operatorname {sgn}(\cos(2x))+1)/2)\ +\ \operatorname {sgn}(\sin(x))((\operatorname {sgn}(-\cos(2x))+1)/2)$

Where sgn is the very useful sign function. There's probably a better way to do this, but hey, it works so far.

The square cosine ("coski") is defined as:

${\mbox{cossq}}(x)={\mbox{sinsq}}(x+\pi /2)$

This page is here just for further references. I'm sure someone else will eventually find it useful. :)