Math

Parametric equations.

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

Real-world.

  • 1 A circle: x = cos(t), y = sin(t) for 0 ≤ t ≤ 2π
  • 2 Projectile motion: x = v₀cos(θ)t, y = v₀sin(θ)t - ½gt²
  • 3 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

Studied in

1 unit use this concept.