Editing Polar coordinate system (section)

==Applications==
Polar coordinates are two-dimensional and thus they can be used only where point positions lie on a single two-dimensional plane. They are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point. For instance, the examples above show how elementary polar equations suffice to define curves—such as the Archimedean spiral—whose equation in the Cartesian coordinate system would be much more intricate. Moreover, many physical systems—such as those concerned with bodies moving around a central point or with phenomena originating from a central point—are simpler and more intuitive to model using polar coordinates. The initial motivation for the introduction of the polar system was the study of [[circular motion|circular]] and [[orbital motion]].

===Position and navigation===
Polar coordinates are used often in [[navigation]] as the destination or direction of travel can be given as an angle and distance from the object being considered. For instance, [[aircraft]] use a slightly modified version of the polar coordinates for navigation. In this system, the one generally used for any sort of navigation, the 0° ray is generally called heading 360, and the angles continue in a clockwise direction, rather than counterclockwise, as in the mathematical system. Heading 360 corresponds to [[magnetic north]], while headings 90, 180, and 270 correspond to magnetic east, south, and west, respectively.<ref>{{Cite web |last=Santhi |first=Sumrit |title=Aircraft Navigation System |url=http://www.thaitechnics.com/nav/adf.html |access-date=2006-11-26}}</ref> Thus, an aircraft traveling 5 nautical miles due east will be traveling 5 units at heading 90 (read [[ICAO spelling alphabet|zero-niner-zero]] by [[air traffic control]]).<ref>{{Cite web |title=Emergency Procedures |url=https://www.faa.gov/regulations_policies/handbooks_manuals/aircraft/airplane_handbook/media/faa-h-8083-3a-7of7.pdf |url-status=dead |archive-url=https://web.archive.org/web/20130603111635/http://www.faa.gov/regulations_policies/handbooks_manuals/aircraft/airplane_handbook/media/faa-h-8083-3a-7of7.pdf |archive-date=2013-06-03 |access-date=2007-01-15}}</ref>

===Modeling===
Systems displaying [[radial symmetry]] provide natural settings for the polar coordinate system, with the central point acting as the pole. A prime example of this usage is the [[groundwater flow equation]] when applied to radially symmetric wells. Systems with a [[central force|radial force]] are also good candidates for the use of the polar coordinate system. These systems include [[gravitation|gravitational fields]], which obey the [[inverse-square law]], as well as systems with [[point source]]s, such as [[antenna (radio)|radio antennas]].

Radially asymmetric systems may also be modeled with polar coordinates. For example, a [[microphone]]'s [[Microphone pick up patterns|pickup pattern]] illustrates its proportional response to an incoming sound from a given direction, and these patterns can be represented as polar curves. The curve for a standard cardioid microphone, the most common unidirectional microphone, can be represented as {{nowrap|''r'' {{=}} 0.5 + 0.5sin(''ϕ'')}} at its target design frequency.<ref>{{Cite book |last=Eargle |first=John |title=Handbook of Recording Engineering |publisher=Springer |year=2005 |isbn=0-387-28470-2 |edition=Fourth |author-link=John M. Eargle}}</ref> The pattern shifts toward omnidirectionality at lower frequencies.