I hope this random thought is on topic. If not please notify me before penalising me for it.
I have reflected that Sin and Cos provide answers for trigonometry problems with cartesian pairs on a 2D plane inside a unit circle.
Why stop there?
Is there a further similar function which adds the z axis so problems can be solved in 3D, inside a unit sphere? If there isn't, is there an explanation for why?
In spherical co-ordinates each point in $\mathbb{R}^3$ has a distance from the origin $r$ and two angles $\theta$ and $\phi$. This is analogous to polar co-ordinates in $\mathbb{R}^2$ except there are two angles instead of one.
Converting to Cartesian co-ordinates, the $x,y,z$ co-ordinates of a point are functions of $r$ and the two angles:
$(x,y,z) = \left(rf(\theta, \phi), \space rg(\theta, \phi), \space rh(\theta, \phi) \right)$
but, as it happens, the functions $f,g,h$ can be expressed simply in terms of $\sin$ and $\cos$:
$f(\theta, \phi)=\sin (\theta) \cos (\phi) \\ g(\theta, \phi)=\sin (\theta) \sin (\phi)\\ h(\theta, \phi)=\cos (\theta)$
As far as I know the functions $f, g, h$ have never been given specific names.