I was thinking about the graphs of different trig functions and noticed that most of them are of a similar shape to some different types of polynomials. For example:
- Higher degree polynomials create a wave like sin or cos
- $x^3$ looks like one repetition of tan, and could be flipped and shifted to look like cot
- Each repetition of sec and csc looks like two quadratic parabolas
While obviously the polynomials aren't going to be an exact approximation, are there a set of coefficients that create a reasonably close (to a few decimal places) approximation of one period of the trig functions?
If so, is this useful? Or are there other, better, post Pre Calculus approximations of the trig functions?