Math Calculators, Lessons and Formulas

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Analytic Geometry: (lesson 4 of 4)

## Polar Coordinates

Each point in the polar coordinate system can be described with the two polar coordinates, which are usually called r (the radial coordinate) and θ (the angular coordinate, polar angle, or azimuth angle, sometimes represented as φ or t). The r coordinate represents the radial distance from the pole, and the θ coordinate represents the anticlockwise (counterclockwise) angle from the 0.

For example, the polar coordinates (3, 6) would be plotted as a point 3 units from the pole on the 6 ray.

### Converting between polar and Cartesian coordinates

From polar to cartesian coordinates.

Example 1:

Convert (3, ) into polar coordinates

Solution:

From cartesian to polar coordinates.

Example 2:

Convert (-1,-1) into polar coordinates

Solution:

### Circle:

This is a circle of radius and center (a, b).