A coordinate system, which uses the distance from the coordinate system center and positional angles to identify points in space rather than orthogonal independent unit vectors as in the Cartesian coordinate system. Polar and partly polar (cylindrical) coordinate systems are widely used to describe spin motion in NMR experiments.
It is important to know how to compute the coordinates of a point in the polar coordinate system when they are given in a Cartesian system and vice versa. The length of the vector r pointing from the coordinate origin to a point in 2D space is given as
r = √(x² + y²).
while the polar or phase angle f is obtained by performing the operation
f = arctan (y/x),
where the arctan function is the inverse of the tangent function.