Spherical coordinates

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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.