poolcoördinaatsysteem

The poolcoördinaatsysteem, or polar coordinate system, is a two-dimensional coordinate system where points are identified by a distance from a central point and an angle from a reference direction. The central point is called the pole or origin, and the reference direction is the polar axis, typically depicted as a horizontal ray extending to the right from the pole.

Each point in the polar coordinate system is represented by an ordered pair (r, θ), where 'r' is the radial coordinate and 'θ' is the angular coordinate. The radial coordinate 'r' represents the directed distance from the pole to the point. The angular coordinate 'θ', often called the azimuth or polar angle, represents the angle measured counterclockwise from the polar axis to the line segment connecting the pole to the point.

Unlike the Cartesian coordinate system (x, y), the representation of a point in polar coordinates is not unique. For example, a point with polar coordinates (r, θ) can also be represented by (r, θ + 2πn) or (-r, θ + π + 2πn), where 'n' is any integer. This non-uniqueness can be useful in certain mathematical contexts.

The polar coordinate system is particularly well-suited for describing phenomena that exhibit rotational symmetry, such as circles, spirals, and certain types of curves and surfaces. It finds applications in various fields including physics, engineering, mathematics, and computer graphics. Converting between polar and Cartesian coordinates is straightforward using trigonometric relationships: x = r cos(θ) and y = r sin(θ) for converting from polar to Cartesian, and r = √(x² + y²) and θ = arctan(y/x) for converting from Cartesian to polar.