# Approximating Trig Functions with Polynomials

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?

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You will learn about Taylor series, which can be used to approximate functions using polynomials in higher calculus courses –  user130512 Feb 25 '14 at 18:30