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