math121 ch923d parametric curves in desmos
Graphing and animating parametric curves in Desmos.
It's also not a bad idea to name your functions X(t) and Y(t) instead of f(t) and g(t), and then make Desmos plot the parametric curve by having a cell that says (X(t),Y(t)). You have to use capital letters X and Y for that, though, not lowercase x(t) and y(t), since Desmos treats lowercase x and y specially.