# Homework Help: Trigonometric polynomial

1. Dec 20, 2007

### quasar987

1. The problem statement, all variables and given/known data
Maybe I'm just blind, but how is

$$T_n(x)=\left(\frac{1+\cos(t-a)}{b}\right)^n$$

of the form

$$T_n(x)=\sum_{k=-n}^nc_ke^{ikx}$$

???

I can get

$$\left(\frac{\cos(t-a)}{b}\right)^n$$

by setting

$$c_{\pm n}=\left(\frac{e^{\mp ia}}{2b}\right)^n$$

and the rest of the c_k= 0, but how does the +1 comes in?

Last edited: Dec 20, 2007
2. Dec 20, 2007

### HallsofIvy

][tex](1+ a)^n= 1+ a+ _nC_2a^2+ ...+ a^{n-1}+ a^n[/itex] by the binomial theorem. Now use what you give to write each term as an exponential.

3. Dec 20, 2007

Ah!

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