 Polar angle

In the usual physics convention for spherical coordinates, the polar angle is the angle between the positive $z$ axis and the position vector. For $r=\sqrt{x^2+y^2+z^2}>0$, it satisfies $\cos \theta =z/r$ with $0\le \theta \le \pi$. The north and south axes have $\theta =0$ and $\theta =\pi$, respectively; the plane $z=0$ has $\theta =\pi /2$. The angle is undefined at the origin. In plane polar coordinates, the same phrase usually denotes the oriented in-plane angle instead, so the reference axis and convention should always be stated. The azimuth supplies the other angular coordinate in three dimensions.