Editing Spherical coordinate system (section)

{{Use American English|date = March 2019}}
{{Short description|Coordinates comprising a distance and two angles}}
[[File:3D Spherical.svg|thumb|The '''''physics convention'''''. Spherical coordinates ('''{{mvar|r}}''', '''{{mvar|θ}}''', '''{{mvar|φ}}''') as commonly used: ([[International Organization for Standardization|ISO]] [[ISO/IEC 80000|80000-2:2019]]): radial distance {{mvar|r}} ([[slant distance]] to origin), polar angle {{mvar|θ}} ([[theta]]) (angle with respect to positive polar axis), and azimuthal angle {{mvar|φ}} ([[phi]]) (angle of rotation from the initial meridian plane). '''''This is the convention followed in this article.''''']]

In [[mathematics]], a '''spherical coordinate system''' specifies a given point in [[three-dimensional space]] by using a distance and two angles as its three [[coordinate system|coordinates]]. These are

* the '''radial distance''' '''{{mvar|r}}''' along the line connecting the point to a fixed point called the [[Origin (mathematics)|origin]];
* the '''polar angle''' '''{{mvar|θ}}''' between this radial line and a given ''polar axis'';{{efn|An [[oriented line]], so the polar angle is an [[oriented angle]] reckoned from the polar axis main [[direction (geometry)|direction]], not its opposite direction.}} and
* the '''azimuthal angle''' '''{{mvar|φ}}''', which is the [[angle of rotation]] of the radial line around the polar axis.{{efn|If the polar axis is made to coincide with positive ''z''-axis, the azimuthal angle ''φ'' may be calculated as the angle between either of the ''x''-axis or ''y''-axis and the [[orthogonal projection]] of the radial line onto the reference ''x-y''-plane {{mdash}} which is [[Orthogonality|orthogonal]] to the ''z''-axis and passes through the fixed point of origin, completing a three-dimensional [[Cartesian coordinate system]].}}

(See graphic regarding the "physics convention".) <!-- Please maintain the bolding of symbols and terms (in the first occurrence only) for ease of distinguishing same while introducing them to reader, but do not forget to also apply italics for scalars. -->

Once the radius is fixed, the three coordinates (''r'', ''θ'', ''φ''), known as a 3-[[tuple]], provide a coordinate system on a [[sphere]], typically called the '''spherical polar coordinates'''.
The [[plane (geometry)|plane]] passing through the origin and [[perpendicular]] to the polar axis (where the polar angle is a [[right angle]]) is called the '''''reference plane''''' (sometimes ''[[fundamental plane (spherical coordinates)|fundamental plane]]'').