From Wikipedia:
A right circular cone with height $h$ and aperture $2\theta$, whose axis is the $z$-coordinate axis and whose apex is the origin, is described parametrically as $$F(s,t,u) = \left(u \tan s \cos t, u \tan s \sin t, u \right),$$ where $s,t,u$ range over $[0,\theta)$, $[0,2\pi)$, and $[0,h]$, respectively.
How is this derived? Can someone walk me through it?