What is the name for each angle in polar coordinates on three dimensions

Question

In polar coordinates each point can be defined by its radius and two angles: $(r,\theta ,\varphi )$, the relationship with the cartesian coordinates can vary but I would use:

$$x=r\sin(\theta)\cos(\varphi) $$ $$y=r\sin(\theta)\sin(\varphi) $$ $$z=r\cos(\theta) $$

I would like to know the name of this angles. I have seen that $\varphi$ is called colatitude or zenith but $\theta$ is just referred as "the angle".

Answer 1

Short and sweet, here's what I've been calling them :

$\theta$ is "polar angle" or "colatitude" $\in [0,\pi]$ (indeed the regular latitude $\in [-\pi/2,\pi/2]$)

$\varphi$ is "azimuth" or "longitude" $\in [0,2\pi]$

I have seen french people call $\theta$ the "zenithal angle" but only rarely

Answer 2

I call your $\theta$ the zenith angle and your $φ$ the azimuth.

Wikipedia offers more suggestions.