Polar coordinates

Math

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

  • (5, π/3) means 5 units from the origin at a 60° angle
  • Converting (3, 4) to polar: r = 5, θ = arctan(4/3)
  • 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)

Related Terms

Polar graphs Unit circle Coterminal angles Degree to radian conversion

Study This Concept

Practice polar coordinates with free review games in these units:

Trigonometry Unit 8: Polar Coordinates and Complex Numbers