Polar Coordinate System


In a polar coordinate system, a fixed point O is called the pole or origin. The polar axis is usually a horizontal ray directed toward the right from the pole. The location of point P in the polar coordinate system can be identified by polar coordinates in the form (r, ). If a ray is drawn from the pole through point P, the distance from the pole to point P is | r |. The measure of the angle formed by ray OP and the polar axis is . The angle can be measured in degrees or radians.

If r is positive, is the measure of any angle in standard position that has ray OP as its terminal side.

If r is negative, is the measure of any angle that has the ray opposite ray OP as its terminal side.


An equation that uses polar coordinates is called a polar equation. For example, is a polar equation. A polar graph represents the solution set which is the set of points whose coordinates (r, ) satisfy a given polar equation.