Math

Polar coordinates.

Definition

A coordinate system that locates points by their distance from the origin (r) and angle from the positive x-axis (θ), written as (r, θ). This is an alternative to the Cartesian (x, y) system.

Examples

Real-world.

  • 1 (5, π/3) means 5 units from the origin at a 60° angle
  • 2 Converting (3, 4) to polar: r = 5, θ = arctan(4/3)
  • 3 Describing circular motion is much simpler in polar form
Key Fact

x = r cos θ, y = r sin θ; r = √(x²+y²), θ = arctan(y/x)