A [[Free Parameter]] of some equation (or [[Function]]) $f$ is some variable(s) typically denoted $t$, $s$, $u$, or $v$. These variables *typically* have no restriction on its [[Domain]] and in the most common examples will be [[Continuous]] input to $f$. Some cases will denote that as a finite range, and these cases are typically ones whose parametric functions are periodic. >[!example] Periodic [[Parametric Function|Parametric Curve]] [[Free Parameter]] >$\huge >f(u,v) = \mat{ r\sin(s) \\ r\cos(t)}\\ >$ >Where $u,v \in [0, 2\pi]$.