# Fourier Series - Am I Crazy or is My Teacher Tricking Me?

1. Nov 3, 2012

### mundane

I am SO annoyed with this problem. Ready to jump out a window.

1. The problem statement, all variables and given/known data

Find the first three terms of the Fourier series that approximates f(θ) = tan(θ) from θ = -π/2 to π/2.

3. The attempt at a solution

So, I know that for an equation on [$\frac{-b}{2}$, $\frac{b}{2}$], to define the Fourier series for that equation we use f(x)={a0+a1cosx+a2cos2x+ ... +b1sinx+b2sin2x+ ...}

I only need to find the first three terms, so its just a0+a1cosx+b1sinx.

a0 is defined as $\frac{1}{\pi}$$\intf(x)dx$ definite integral from -π/2 to π/2.

a1 is defined as $\frac{2}{\pi}$$\int\f(x)cos(2πx/π)dx$ definite integral from -π/2 to π/2.

b1 is defined as $\frac{2}{\pi}$$\int\f(x)sin(2πx/π)dx$ definite integral from -π/2 to π/2.

For a0, my antiderivative was -log(cos(x)). After substitution, a0=0.

For a1, my antiderivative was log(cos(x))-(1/2)cos(2x). After substitution, a1=0.

I have not done b1 yet. Am I being trolled?

Does this ave something to do with the fact that tan(x) is undefined at those two interval points? Am I going in the wrong direction???

2. Nov 3, 2012

### aralbrec

If a function is odd, can it have cosine terms?
If a function is even, can it have sine terms?

3. Nov 3, 2012

4. Nov 3, 2012

### mundane

Sorry, I didn't mean to repost. I was trying to change the red font and it reposted. Sorry.

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