# Trig homework problem

1. Oct 29, 2006

### Dragonfall

How do I show that

$$T_n(x)=\cos(n\arccos(x))$$

are actually polynomials of degree n?

If n=2 then

$$T_2(x)=x^2-(1-x^2)$$

but this seems to break down as n increases.

2. Oct 29, 2006

### StatusX

So if x=cos(y), you want to show cos(ny) is a nth degree polynomial in cos(y). Induction is usually the first thing to try whenever there's an n knocking about.

3. Oct 29, 2006

### Office_Shredder

Staff Emeritus
It also definitely fails for n=1, but since you started with 2, maybe we're ignoring that

4. Oct 29, 2006

### d_leet

How does it fail for n=1? The function f(x)=x is a polynomial.