Poolcoördinatensysteem

Poolcoördinatensysteem refers to a system of coordinates used to describe the position of points in a two-dimensional space. It is also known as the polar coordinate system. In this system, a point is defined by its distance from a central point, called the pole, and an angle measured from a reference direction, called the polar axis. The distance from the pole is typically denoted by the radial coordinate, often represented by 'r', and the angle is usually represented by the angular coordinate, often denoted by 'θ' (theta).

The pole is usually placed at the origin of a Cartesian coordinate system, and the polar axis is typically aligned with the positive x-axis. The angle is measured counterclockwise from the polar axis. A point with polar coordinates (r, θ) can be converted to Cartesian coordinates (x, y) using the relationships x = r cos(θ) and y = r sin(θ). Conversely, Cartesian coordinates can be converted to polar coordinates using r = sqrt(x^2 + y^2) and θ = atan2(y, x). The function atan2(y, x) is used to correctly determine the angle in all four quadrants.

Poolcoördinatensysteem is particularly useful in describing circular or spiral phenomena, such as orbits, waves, and rotating objects. It simplifies many mathematical operations, especially those involving rotations or symmetry around a central point. While a unique representation is desirable, it's important to note that a single point in polar coordinates can have multiple representations due to the periodic nature of angles. For instance, (r, θ) is the same point as (r, θ + 2πn) for any integer n.