**Relation to trigonometric
functions.**

The signal property of Chebyshev
polynomials is the trigonometric representation on
[-1,1].

Consider the following expansion using the *Mathematica* command
"FunctionExpand."

**Exploration 2.**

We are interested in the polynomial form of Cos[n ArcCos[x]], however we will restrict our analysis to [-1,1].

Here is a list of several expansions.

(c) John H. Mathews 2004