What are polar coordinates?
A point given by its distance r from the origin and the angle θ from the positive x-axis, written (r, θ), instead of by (x, y).
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Polar Coordinates
Convert between polar (r, θ) and rectangular (x, y) coordinates both ways, plotted on a polar grid, with θ in degrees or radians.
x = r cos θ, y = r sin θ; r = √(x²+y²), θ = atan2(y, x)
A mind behind this: Leonhard Euler 1707–1783
Angle unit
Frequently asked questions
How do I convert between forms?
Polar to rectangular: x = r cos θ, y = r sin θ. Rectangular to polar: r = √(x² + y²) and θ = atan2(y, x), which gives the correct quadrant.
Can you show a worked example?
(r, θ) = (5, 53.13°) gives x = 5 cos 53.13° ≈ 3 and y = 5 sin 53.13° ≈ 4. In radians 53.13° ≈ 0.9273 rad; the toggle shows θ that way.
Why use atan2 instead of arctan?
arctan(y/x) loses the quadrant, so a point in the third quadrant could be confused with the first. atan2(y, x) uses both signs to return the correct angle.
Where are polar coordinates used?
Radar and navigation, circular and spiral motion, and curves like cardioids and roses that are far simpler in polar form.