# Spherical coordinates

From AMS Glossary

(Redirected from Polar angle)

## spherical coordinates

(

*Also called*polar coordinates in space, geographical coordinates.) A system of curvilinear coordinates in which the position of a point in space is designated by its distance*r*from the origin or pole along the radius vector, the angle φ between the radius vector and a vertically directed polar axis called the cone angle or colatitude, and the angle θ between the plane of φ and a fixed meridian plane through the polar axis, called the polar angle or longitude.A constant-amplitude radius vector

**r**confines a point to a sphere of radius*r*about the pole. The angles φ and θ serve to determine the position of the point on the sphere. The relations between the spherical coordinates and the rectangular Cartesian coordinates (*x*,*y*,*z*) are*x*=*r*cos θ sin φ;*y*=*r*sin θ sin φ;*z*=*r*cos φ.