Ympyräkoordinaatistossa

Ympyräkoordinaatistossa, also known as polar coordinates, is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point, called the pole, and an angle from a fixed direction, called the polar axis. The pole is typically represented by the origin (0,0) in Cartesian coordinates, and the polar axis is usually aligned with the positive x-axis.

In polar coordinates, a point is represented by an ordered pair (r, θ), where r is the radial coordinate or radius, and θ is the angular coordinate or angle. The radius r is the distance from the pole to the point, and the angle θ is the counterclockwise rotation from the polar axis to the line connecting the pole to the point.

The conversion between polar and Cartesian coordinates is straightforward. Given a point (r, θ) in polar coordinates, the corresponding Cartesian coordinates (x, y) can be found using the following formulas:

x = r * cos(θ)

y = r * sin(θ)

Conversely, given a point (x, y) in Cartesian coordinates, the corresponding polar coordinates (r, θ) can be found using the following formulas:

r = sqrt(x^2 + y^2)

θ = atan2(y, x)

Polar coordinates are particularly useful in situations where the radial distance and angular direction are more natural or convenient to use than Cartesian coordinates. They are commonly used in fields such as physics, engineering, and computer graphics.