Polarvinkel

Polarvinkel is a term used for the angular coordinate that specifies direction in polar and related coordinate systems. In two-dimensional polar coordinates a point is represented by (r, θ), where r is the radial distance from the origin and θ (the polarvinkel) is the angle measured from a chosen reference axis, usually the positive x-axis. Cartesian conversion is given by x = r cos θ and y = r sin θ. The polarvinkel is periodic with period 2π and is customarily expressed in radians or degrees; common principal ranges are 0 ≤ θ < 2π or −π < θ ≤ π.

Determining the correct quadrant when computing θ from Cartesian coordinates uses the two-argument arctangent function, atan2(y, x), which handles sign and branch choices. The polarvinkel is multivalued in that θ and θ + 2πk represent the same direction; specifying a principal value fixes a single representative.

In three-dimensional systems the term may cause ambiguity: in spherical coordinates one angle is sometimes called the polar angle (colatitude), measured from the positive z-axis and ranging from 0 to π, while the other is the azimuthal angle in the x–y plane. Polarvinkel appears in mathematics, physics, engineering and navigation (where related concepts include bearing and azimuth) and is fundamental to expressing curves, fields and complex numbers in angular form.