## Polar Coordinates

The polar coordinates and are defined by

 (1) (2)

In terms of and ,
 (3) (4)

The Arc Length of a polar curve given by is
 (5)

The Line Element is given by
 (6)

and the Area element by
 (7)

The Area enclosed by a polar curve is
 (8)

The Slope of a polar function at the point is given by
 (9)

The Angle between the tangent and radial line at the point is
 (10)

A polar curve is symmetric about the -axis if replacing by in its equation produces an equivalent equation, symmetric about the -axis if replacing by in its equation produces an equivalent equation, and symmetric about the origin if replacing by in its equation produces an equivalent equation.

In Cartesian coordinates, the Position Vector and its derivatives are

 (11) (12) (13) (14)

In polar coordinates, the Unit Vectors and their derivatives are

 (15) (16) (17) (18) (19) (20)

See also Cardioid, Circle, Cissoid, Conchoid, Curvilinear Coordinates, Cylindrical Coordinates, Equiangular Spiral, Lemniscate, Limaçon, Rose