# Polar Coordinates

You can specify the position of a point in a Cartesian plane by specifying its distance, R, from the origin, and the angle to the positive x-axis in a counterclockwise direction, the angle α.

If you right-click on a point in the algebra view you can choose to show the polar coordinates instead of the Cartesian coordinates. GeoGebra writes polar coordinates by using a semi-colon instead if a comma.

If you want to enter a point using polar coordinates in the input bar, use a semi-colon.

A=(2;30°)

The degree-symbol can be found in the symbol-menu beside the input bar, it can also be written Ctrl+o.

## Epitrochoids using polar coordinates

As an example of how to use polar coordinates, the model of the sun, earth, and moon will be used. See GeoGebra Tutorial - Epicycles.

Input a slider `R` for the radius of the earth's orbit around the sun, and a slider `r` for the radius of the moon's orbit around the earth. Input a slider `α` to denote the angle and a slider `months` to denote the number of months in a year. Let `A` denote the earth, and `B` the moon . The coordinates of the points can be entered in polar form as:

```	A=(R;α)
B=A+(r;months*α)
```

Put a trace on `B`. It is also possible to show the locus of `B`, click on the Locus tool, then on `B`, then on the slider `α`.