Question

in spherical polar coordinates how angle theeta varies from 0 to 180

Answer 1

http://mathinsight.org/spherical_coordinates

http://www.pha.jhu.edu/~javalab/spherical/spherical.html

Answer 2

What angle is theta in your textbook?

If it is colatitude, yes, it varies from 0 (North pole) to 180° (South pole) through 90) (Equator)

If it is longitude, it varies from -180° to +180°

Answer 3

I'm asking, because, Festinger's link has theta and phi one way, whereas Wikipedia has the opposite.
http://en.wikipedia.org/wiki/Spherical_coordinates

Answer 4

This is how I learned the angles of spherical coordinates to be, and I've seen different reliable sources interchange \(\theta\) and \(\phi\).

For mine, I will use \(\theta\) like you do for polar coordinates: on the \(xy\)-plane.How I learned it, \(\theta\) is measured from the positive \(x\)-axis and increases in the direction of the positive \(y\)-axis.

That leaves \(\phi\) to be from the positive \(z\)-axis and increases in the direction of the point. That means, \(\phi\) increases toward the \(xy\)-plane in the direction of \(\theta\), in the way I learned it.

Now, for the ranges, you can have both \(\theta\) and \(\phi\) got from \(0\rightarrow 360^\circ\), a.k.a. \(0\rightarrow 2\pi\ [radians]\). But you can get to all the points without having both in that range. So I learned to do what @Vincent-Lyon.Fr did.

You can use all of your angles on the \(xy\) plane, all \(360^\circ\) or \(2\pi\ [rad]\), then all you need is up and down. All the up and down can be covered with the angles from the \(z\)-axis, with straight up being \(0^\circ=0\ [rad]\), and straight down being \(180^\circ=\pi\ [rad]\).

\(\Large \mathsf{Summary:}\)
So the angle is from \(0\rightarrow 180^\circ\), a.k.a. \(0\rightarrow \pi\ [rad]\), because that's all you need when the angles in the \(xy\)-plane cover all \(360^\circ\) or \(2\pi\ [rad]\).