🚀 go-pugleaf

Some time ago, I asked for net-wisdom on the subject of constrained
least squares.  Many of you responded, letting me know that I was
on track.  First, let me thank all those who responded.  I've since
written my own little program to do constrained least square fits
of n-degree polynomials.  But now I have a slightly off-the-wall
question for you.  Read on. ;-)

Given some explicitely defined function g(x), say, g(x) = sin(x),
can the method of least square errors be applied such that
we derive a second function f(x) = a0 + a1*x + a2*x^2 + ... + an*x^n  
where f(x) is the best least squares fit to g(x)?

I know that this request sounds strange.  But I have a legitimate
application.  The application software that I'm using, ANSYS, 
forces me to input certain quantities as polynomial functions
of temperature.  So I can't get around using a polynomial.
Given this restriction, I at least want to use a best-fit polynomial.

Has anyone ever heard of this being done before?

Tony Rizzo