I am SO annoyed with this problem. Ready to jump out a window.(adsbygoogle = window.adsbygoogle || []).push({});

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 [[itex]\frac{-b}{2}[/itex], [itex]\frac{b}{2}[/itex]], to define the Fourier series for that equation we use f(x)={a_{0}+a_{1}cosx+a_{2}cos2x+ ... +b_{1}sinx+b_{2}sin2x+ ...}

I only need to find the first three terms, so its just a_{0}+a_{1}cosx+b_{1}sinx.

a_{0}is defined as [itex]\frac{1}{\pi}[/itex][itex]\int\f(x)dx[/itex] definite integral from -π/2 to π/2.

a_{1}is defined as [itex]\frac{2}{\pi}[/itex][itex]\int\f(x)cos(2πx/π)dx[/itex] definite integral from -π/2 to π/2.

b_{1}is defined as [itex]\frac{2}{\pi}[/itex][itex]\int\f(x)sin(2πx/π)dx[/itex] definite integral from -π/2 to π/2.

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

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

I have not done b_{1}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???

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

2. Relevant equations

3. The attempt at a solution

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

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