Polar Coordinates

The polar coordinates r (the radial coordinate) and theta (the angular coordinate, often called the polar angle) are defined in terms of Cartesian coordinates by:

 x = rcostheta (1) y = rsintheta

where r is the radial distance from the origin, and theta is the counterclockwise angle from the x-axis. In terms of √(x^2+y^2) (3) theta = tan^(-1)(y/x). (4) (Here, tan^(-1)(y/x) should be interpreted as the two-argument inverse tangent which takes the signs of x and y into account to determine in which quadrant theta lies.) It follows immediately that polar coordinates aren't inherently unique; in particular, (r,theta+2npi) will be precisely the same polar point as (r,theta) for any integer n. What's more, one often allows negative values of r under the assumption that (-r,theta) is plotted identically to (r,theta+/-pi).

We start with a cartesian coordinate system. We choose O as pole and the x-axis as polar-axis. The cartesian coordinates of a point P are (x,y). Choose the u-axis such that r > 0. then P = r U => P2 = r2 U2 => x2 + y2 = r2 r = sqrt(x2 + y2) Now, choose a t-value such that x = r.cos t and y = r.sin t