# Definition of polar coordinates in US English:

## polar coordinates

### plural noun

Geometry
• 1A pair of coordinates locating the position of a point in a plane, the first being the length of the straight line (r) connecting the point to the origin, and the second the angle (θ) made by this line with a fixed line.

• ‘The same formula can be expressed in polar coordinates, where the locations of points are expressed in terms of angle, q, and distance, r, from the origin rather than x and y coordinates.’
• ‘Cartesian and polar coordinates are great tools in the analytic geometry of the plane.’
• ‘It was based on polar coordinates whereas earlier instruments were based on cartesian coordinates.’
• ‘On page 149, Pesic mentions de Moivre's discovery of the formula (cos [theta] + i sin [theta]) n = cos n [theta] + i sin n [theta] and implies that to prove it one needs to think about complex numbers in polar coordinates.’
• ‘If we insist on unbiasedness, we must choose c so that E = [mu] uniformly in [mu]. To think about that, we first express the problem in polar coordinates.’
1. 1.1 The coordinates in a three-dimensional extension of this system.
• ‘Since the profile is a curved shape, it's much easier mathematically to use what are known as as polar coordinates.’