# Wolfram Mathematica

## Polar and Spherical Coordinates

New, dedicated functions are available to convert between Cartesian and the two most important non-Cartesian coordinate systems: polar coordinates and spherical coordinates.

Convert between Cartesian and polar coordinates.

In[1]:=
`ToPolarCoordinates[{x, y}]`
Out[1]=
In[2]:=
`FromPolarCoordinates[{r, \[Theta]}]`
Out[2]=

Convert between Cartesian and spherical coordinates.

In[3]:=
`ToSphericalCoordinates[{x, y, z}]`
Out[3]=
In[4]:=
`FromSphericalCoordinates[{r, \[Theta], \[CurlyPhi]}]`
Out[4]=

Polar coordinates naturally generalize to higher dimensions.

In[5]:=
`ToPolarCoordinates[{w, x, y, z}]`
Out[5]=
In[6]:=
```FromPolarCoordinates[{r, \[Theta]1, \[Theta]2, \[Theta]3, \ \[CurlyPhi]}]```
Out[6]=

Plot curves expressed in polar and spherical coordinates.

In[7]:=
```ParametricPlot[ FromPolarCoordinates[{Exp[-t/10], t}] // Evaluate, {t, 0, 50}, PlotRange -> All]```
Out[7]=
In[8]:=
```ParametricPlot3D[ FromSphericalCoordinates[{1, TriangleWave[{0, Pi}, p/(2 Pi)], p}] // Evaluate, {p, 0, 2 Pi}]```
Out[8]=