Given a variable point with a boundary restriction how can i find the line that matches the point boundary?

Question

I'd like to start off by asking anyone who knows how to better phrase this question to improve it, as I don't know how to phrase this question well. Essentially, if i'm given some variable n, and we create a point that follows the rule $$(n, a(n))$$ how could i find the equation for the line that matches this point set? a good example is $$\left(\operatorname{sin}\left(n\right)+n,\operatorname{cos}\left(n\right)\right) \mbox{for } n= \left[-\infty...\infty\right]$$ which will trace the path of a cycloid. so, given this set of points how would you derive a function f(x) (in this case, the function for a cycloid) that is identical?