Topic: Parametric Equations

When: Friday, April 23 @ 11:00am

Who: Professor Dan Balaguy

Where: Canvas (https://sierra.instructure.com/courses/347458)

A parametric equation defines a group of quantities as functions of one or more independent variables called parameters.[1] Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a parametric representation or parameterization (alternatively spelled as parametrisation) of the object.[1][2][3]

For example, the equations

{\displaystyle {\begin{aligned}x&=\cos t\\y&=\sin t\end{aligned}}}

form a parametric representation of the unit circle, where t is the parameter: A point (x, y) is on the unit circle if and only if there is a value of t such that these two equations generate that point. Sometimes the parametric equations for the individual scalar output variables are combined into a single parametric equation in vectors:

${\displaystyle (x,y)=(\cos t,\sin t).}$