Parametric Equations (Edexcel A-Level Mathematics): Flashcards

$x$ and $y$ are functions of a parameter $t$: $x=f(t)$, $y=g(t)$.

Choose a range for the parameter $t$ based on the context.

Calculate corresponding values for selected $t$ within the range.

Plot points in the order $t$ increases to show curve direction.

Connect the points smoothly, indicating direction with an arrow.

Mark intercepts, maxima, minima, and changes of direction.

Set $x(t) = 0$ or $y(t) = 0$ and solve for $t$.

$x=\cos(t)$, $y=\sin(t)$ for $t$ in $[0, 2\pi]$.

$x = a \cos(t)$, $y = b \sin(t)$ for $t$ in $[0, 2\pi]$.

It allows flexible description of curves not easily expressed.