Modelling with Parametric Equations (Edexcel A-Level Mathematics): Flashcards

They model relationships using a third parameter, often time.

As functions of a third variable $t$: $x = f(t)$, $y = g(t)$.

The horizontal distance travelled in projectile motion.

$y(t) = v_0 \sin(\theta) \cdot t - 0.5gt^2$.

The resulting curve is a parabola.

Set $dy/dt = 0$ and solve for $t$, then substitute in $y(t)$.

$x(t) = r \cos(\omega t)$ and $y(t) = r \sin(\omega t)$.

$x(t) = a \cos(t)$ and $y(t) = b \sin(t)$.

Typically, $t$ represents time in parametric equations.

They can represent complex curves difficult for Cartesian.