Spherical Coordinates Confusion: Which Set is Correct?

[kkz23691]

I am accustomed to
$x=rcos(\theta)sin(\phi)$
$y=rsin(\theta)sin(\phi)$
$z=rcos(\phi)$
$-\pi<\theta<\pi$, $-\pi/2 < \phi < \pi/2$

but see some people using these instead
$x=rcos(\theta)cos(\phi)$
$y=rsin(\theta)cos(\phi)$
$z=rsin(\phi)$
$-\pi<\theta<\pi$, $-\pi/2 < \phi < \pi/2$

Have you seen this before?
The second set seems to be "oblate spheroidal coordinates" (http://en.wikipedia.org/wiki/Oblate_spheroidal_coordinates) in the limit where the oblate spheroid is actually a sphere (the argument of the hyperbolic sin/cos is large enough so that
$asinh(\mu)=acosh(\mu)=r=\mbox{const}$

Does this make sense?

 

[jedishrfu]

Yes, if the phi angle is measured relative to the XY plane.

In normal spherical coordinates it is measured relative to the Z axis.

For oblate coordinates see this article:

http://en.wikipedia.org/wiki/Oblate_spheroidal_coordinates

 

[kkz23691]

Thanks jedishrfu, I just checked one article that uses these and indeed, the $\phi$ angle is relative to the XY-pane! Also, some use
x=rcos(θ)cos(ϕ)
y=rsin(θ)cos(ϕ)
z=-rsin(ϕ)
−π<θ<π, −π/2<ϕ<π/2
which probably work fine, even though the "minus" sign in z doesn't match the definition of "oblate spheroidal coordinates" (because the hyperbolic functions are assumed positive there)

If
z=-rsin(ϕ)

doesn't seem right, please post.

 

[HallsofIvy]

I have always seen $\rho$ rather than r but using $\phi$ to mean the angle a line from the origin to the point makes with the z-axis is a "mathematics" notation while using $\theta$ for that is a "physics" notation.

 

[kkz23691]

Yes HallsofIvy certainly agree with you! What was new to me - measuring the inclination w/respect to xy-plane; I guess this is a "geography" notation :)