Close this window

Polar Coordinates

In a plane, suppose you have a point O called the origin, and an axis through that point – say the x-axis – called the polar axis.

Then the polar coordinates (r, θ) describe the point lying a distance of r units away from the origin, at an angle of θ to the x-axis. The value of θ may be given in degrees or radians.

To convert from polar coordinates to Cartesian coordinates, you can use:

x = r cos θ

y = r sin θ

To convert from Cartesian coordinates to polar coordinates:

.

Since .

So, the Cartesian ordered pair (x, y) converts to the Polar ordered pair .