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 Skip Navigation LinksMath Help > Geometry > Polar Coordinates > Conversion between Polar and Rectangular

Polar coordinates of a point are given by (θ, r), where θ is the argument (angle) of the point, and r is the modulus (distance from the origin) of the point.

Rectangular coordinates are given by (x, y), which represent the signed distance of the points from the two orthogonal axes.

Polar equations usually use θ as the independent variable, and r as a function of θ.

Rectangular equations usually use x as the independent variable, and y as a function of x.

I find it interesting that a point specified using rectangular format lists the independent variable first, but a point specified using polar coordinates lists the independent variable last.

Also, it is interesting that the equations that help you convert points from rectangular to polar specification also help you convert equations from polar to rectangular format.  So you can't just say, for example, that r²=x�+y� converts from rectangular to polar.  You have to also say whether you intend to convert equations or points.

Conversion of points from rectangular to polar;
conversion of equations from polar to rectangular;
Conversion of points from polar to rectangular;
conversion of equations from rectangular to polar;
r�=x�+y�
θ=tan-1(y/x)
θ=cos-1(x/r)
θ=sin-1(y/r)
x=r cos(θ)
y=r sin(θ)

Related Pages in this website

Back to Polar Coordinates, or all the way back to Geometry and Trig

The quadrifolium is defined in the Geometry Glossary.


The webmaster and author of this Math Help site is Graeme McRae.