I've been using quite a few 3D parametric curves recently, where the X, Y, and Z components are defined by some function of t. For example:
$t\in\{-\pi,\pi\}$
$x=sin(2t)$
$y=sin(t)$
$z=sin(t)$
To create a simple curve like this:
I'm guessing a curve like this has a name, but I don't know what references I could use to find it. Are there any references that list names for 3d parametric curves like the one above?

I believe these are called "Lissajous Curves". A reference you may consider for looking up different curves: A Catalog of Special Plane Curves by J. Dennis Lawrence.