Poolcoördinatenstelsel

Poolcoördinatenstelsel, also known as polar coordinates, is a two-dimensional coordinate system in which each point is determined by a distance from a fixed origin and an angle from a fixed ray. The origin is called the pole, and the fixed ray is called the polar axis.

In a poolcoördinatenstelsel, a point is represented by an ordered pair (r, θ), where 'r' is the radial distance from the pole to the point, and 'θ' is the angle measured counterclockwise from the polar axis to the line segment connecting the pole to the point. The angle 'θ' is typically measured in radians or degrees.

The relationship between poolcoördinatenstelsel and Cartesian coordinates (x, y) is given by the following equations:

x = r * cos(θ)

y = r * sin(θ)

Conversely, if you have Cartesian coordinates, you can find the polar coordinates using:

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

θ = atan2(y, x)

Poolcoördinatenstelsels are particularly useful for describing phenomena that exhibit rotational symmetry, such as circles, spirals, and certain types of curves. They simplify the representation and analysis of these shapes compared to using Cartesian coordinates. For example, a circle centered at the origin with radius 'a' is simply represented as r = a in polar coordinates, whereas in Cartesian coordinates, it is x^2 + y^2 = a^2. This demonstrates the elegance and efficiency of the polar coordinate system in specific contexts.

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