# Polar

## 2D Coordinate Systems

#### Description

The Polar is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction.
The Polar coordinate system is extended into three dimensions with two different coordinate systems, the cylindrical and spherical coordinate system.

### Mapping

\{x\to r \cos (\phi ),y\to r \sin (\phi )\}
$<mrow> <mo>{</mo> <mrow> <mrow> <mi>x</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>r</mi> <mo>&#8290;</mo> <mrow> <mi>cos</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>&#981;</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>y</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>r</mi> <mo>&#8290;</mo> <mrow> <mi>sin</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>&#981;</mi> <mo>)</mo> </mrow> </mrow> </mrow> </mrow> <mo>}</mo> </mrow>$
{x -> r*Cos[\[Phi]], y -> r*Sin[\[Phi]]}
[x = r*cos(phi), y = r*sin(phi)]

### Cite this as:

2D Coordinate Systems: Polar from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/2DCoordinateSystems/Polar.php