Discover the Fourier Series of (sin x)^2 with Helpful Tips!

[calcgirl]

fourier series, please help!

Homework Statement

Find the Fourier series of f(x)=(sin x)^2.

Homework Equations

The Attempt at a Solution

I know that I need to use the double angle formulas for this problem:
(sin x)^2=1/2-1/2(cos 2x)
but I do not know where to go from here.

 

[quasar987]

All you have to do is calculate the coefficients of the Fourier series... which boils down to computing an integral. See your notes.

 

[calcgirl]

I was told that no integration was needed for this problem and it basically boils down to trig identities.

 

[Alex6200]

Do you know what the Fourier Series is for cos(x)? I'd imagine you could just do you substitution and then use Fourier tables and the like to make that entire thing a Fourier series.

 

[Dick]

I was told that no integration was needed for this problem and it basically boils down to trig identities.

When you used the trig identity you have already written down the cosine series. It has a cos(0*x) term and a cos(2*x) term. What are the coefficients? That IS a Fourier series. Do you want it in some other form?

 

[HallsofIvy]

Definitely no integration is needed for this problem. Do you understand what a Fourier series is? It is a sum of functions of the form cos(nx) and sin(nx)! What is the Taylor's series, about x= 1 for (x-1)²? What is the Fourier seiries for cos(x)? What is the Fourier series for sin(2x)?