Editing Spherical coordinate system (section)

=== Conventions ===
Several different conventions exist for representing spherical coordinates and prescribing the naming order of their symbols. The 3-tuple number set <math>(r,\theta,\varphi)</math> denotes radial distance, the polar angle{{mdash}}"inclination", or as the alternative, "elevation"{{mdash}}and the azimuthal angle. It is the common practice within the physics convention, as specified by [[International Organization for Standardization|ISO]] standard [[ISO 80000-2|80000-2:2019]], and earlier in [[ISO 31-11]] (1992). 

''As stated above, this article describes the ISO "physics convention"{{mdash}}unless otherwise noted.''

However, some authors (including mathematicians) use the symbol ''ρ'' (rho) for radius, or radial distance, ''φ'' for inclination (or elevation) and ''θ'' for azimuth{{mdash}}while others keep the use of ''r'' for the radius; all which "provides a logical extension of the usual polar coordinates notation".<ref name="http://mathworld.wolfram.com/SphericalCoordinates.html">{{cite web |url=http://mathworld.wolfram.com/SphericalCoordinates.html |title=Spherical Coordinates |author=[[Eric W. Weisstein]] |publisher=[[MathWorld]] |date=2005-10-26 |access-date=2010-01-15}}</ref> As to order, some authors list the azimuth ''before'' the inclination (or the elevation) angle. Some combinations of these choices result in a [[right-hand rule|left-handed]] coordinate system. The standard "physics convention" 3-tuple set <math>(r,\theta,\varphi)</math> conflicts with the usual notation for two-dimensional [[polar coordinate system|polar coordinates]] and three-dimensional [[cylindrical coordinate system|cylindrical coordinates]], where {{mvar|θ}} is often used for the azimuth.<ref name="http://mathworld.wolfram.com/SphericalCoordinates.html" />

Angles are typically measured in [[Degree (angle)|degrees]] (°) or in [[radian]]s (rad), where 360°&nbsp;=&nbsp;2{{pi}} rad. The use of degrees is most common in geography, astronomy, and engineering, where radians are commonly used in mathematics and theoretical physics. The unit for radial distance is usually determined by the context, as occurs in applications of the 'unit sphere', see [[#Applications|applications]].

When the system is used to designate physical three-space, it is customary to assign positive to azimuth angles measured in the ''counterclockwise'' sense from the reference direction on the reference plane{{mdash}}as seen from the "zenith" side of the plane. This convention is used in particular for geographical coordinates, where the "zenith" direction is [[north]] and the positive azimuth (longitude) angles are measured eastwards from some [[prime meridian]].

{| class="wikitable" style="text-align:center"
|+ Major conventions
|-
! coordinates set order !! corresponding local geographical directions <br /> {{math|(''Z'', ''X'', ''Y'')}} !! right/left-handed
|-
| {{math|(''r'', ''θ''<sub>inc</sub>, ''φ''<sub>az,right</sub>)}} || {{math|(''U'', ''S'', ''E'')}} || right
|-
| {{math|(''r'', ''φ''<sub>az,right</sub>, ''θ''<sub>el</sub>)}}|| {{math|(''U'', ''E'', ''N'')}} || right
|-
| {{math|(''r'', ''θ''<sub>el</sub>, ''φ''<sub>az,right</sub>)}}|| {{math|(''U'', ''N'', ''E'')}} || left
|}
'''Note:''' [[Easting and northing|Easting ({{mvar|E}}), Northing ({{mvar|N}})]], Upwardness ({{mvar|U}}). In the case of {{math|(''U'', ''S'', ''E'')}} the local [[azimuth]] angle would be measured [[counterclockwise]] from {{mvar|S}} to {{mvar|E}}.