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In [[mathematics]], the '''[[polar coordinate system]]''' is a [[dimension|two-dimensional]] [[coordinate system]] in which each [[point (mathematics)|point]] on a [[plane (mathematics)|plane]] is determined by an [[angle]] and a [[distance]]. The polar coordinate system is especially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance; in the more familiar [[Cartesian coordinate system|Cartesian]] or rectangular coordinate system, such a relationship can only be found through [[trigonometry|trigonometric]] formulation.
As the coordinate system is two-dimensional, each point is determined by two polar coordinates: the radial coordinate and the angular coordinate. The radial coordinate (usually denoted as <math>r</math>) denotes the point's distance from a central point known as the ''pole'' (equivalent to the ''origin'' in the Cartesian system). The angular coordinate (also known as the polar angle or the [[azimuth]] angle, and usually denoted by θ or <math>t</math>) denotes the [[Positive angle#Conventions on measurement|positive]] or [[clockwise|anticlockwise]] (counterclockwise) angle required to reach the point from the 0° [[ray (geometry)|ray]] or ''polar axis'' (which is equivalent to the positive [[x-axis]] in the Cartesian coordinate plane).
Revision as of 00:36, 8 January 2014
A polar grid
In mathematics, the polar coordinate system is a two-dimensionalcoordinate system in which each point on a plane is determined by an angle and a distance. The polar coordinate system is especially useful in situations where the relationship between two points is most easily expressed in terms of angles and distance; in the more familiar Cartesian or rectangular coordinate system, such a relationship can only be found through trigonometric formulation.
As the coordinate system is two-dimensional, each point is determined by two polar coordinates: the radial coordinate and the angular coordinate. The radial coordinate (usually denoted as ) denotes the point's distance from a central point known as the pole (equivalent to the origin in the Cartesian system). The angular coordinate (also known as the polar angle or the azimuth angle, and usually denoted by θ or ) denotes the positive or anticlockwise (counterclockwise) angle required to reach the point from the 0° ray or polar axis (which is equivalent to the positive x-axis in the Cartesian coordinate plane).
