Parametric equations

Math

Definition

A pair of equations that express x and y coordinates separately as functions of a third variable, usually t (the parameter). They allow you to describe curves that may not pass the vertical line test as a single function.

Examples

  • A circle: x = cos(t), y = sin(t) for 0 ≤ t ≤ 2π
  • Projectile motion: x = v₀cos(θ)t, y = v₀sin(θ)t - ½gt²
  • A cycloid traced by a point on a rolling wheel
Key Fact

To eliminate the parameter, solve one equation for t and substitute into the other

Related Terms

Polar coordinates Domain and range Composition of functions

Study This Concept

Practice parametric equations with free review games in these units:

Pre-Calculus Unit 6: Vectors and Parametric Equations