In the United States, polar coordinates are usually written as ($r$,$\theta$). In order to agree with these conventions in the equatorial plane, most American math textbooks use $\theta$ for the azimuthal angle (longitude), and choose some letter other than $r$, usually $\rho$, for the radial coordinate, leaving $\phi$ for the polar angle (colatitude). Almost everyone else reverses the roles of $\theta$ and $\phi$; there are also several different conventions used for the radial coordinate.
On top of this, many American calculus texts list the coordinates in the wrong order, listing longitude before colatitude -- making the coordinate system left-handed. While this causes no difficulty in calculus classes, it is a disaster for subsequent physics and engineering courses which make use of an orthonormal basis adapted to spherical coordinates.
Is there a way out of this mess?
We think so.
First of all, everybody agrees on the conventions for spherical harmonics, the solutions of the angular part of Laplace's equation in spherical coordinates. These functions are written as $Y_{lm}(\theta,\phi)$, where $\theta$ is the polar angle and $\phi$ is the azimuthal angle — just the opposite of the math conventions.
We believe it would be easier to change the conventions used in calculus texts than to change the convention used for spherical harmonics. And all those books with left-handed coordinate systems really need to change anyway. But what about the resulting mismatch between the letters used to denote longitude and the angle in polar coordinates? We would resolve this by using ($r$,$\phi$) for polar coordinates.
We realize that this proposal is unlikely to be popular among American mathematicians. But almost everybody else already uses these conventions at least for spherical coordinates, and many use them for polar coordinates as well, especially outside America.