Conversion from explicit to parametric function

Question

I was given this question:

Given an explicit function $y = \cos(x)$, propose how to convert it to the respective parametric functions $x = f_1(t)$, $y = f_2(t)$?

But I not sure how to solve it. Any ideas or links I could refer to?

Thanks!

Answer 1

The trivial parametrization $\,f_1(t)=t\,$, $\,f_2(t) = \cos(t)\,$ will work, unless there are more constraints.

More generally, $\,f_2(t)=\cos\big(f_1(t)\big)\,$ will work for any bijection $\,f_1 : \mathbb{R} \to \mathbb{R}\,$.