Polar coordinates

A direction and a distance

(r, θ) means go out r from the origin at angle θ, instead of across x and up y.

Converting

x = r cosθ and y = r sinθ. Coming back: r = √(x² + y²) and θ = tan⁻¹(y/x), checking which quadrant you are in.

The same point many ways

(2, π/4) and (2, 9π/4) are the same place, and so is (−2, 5π/4). Polar coordinates are not unique, which is why polar graphs can trace over themselves.