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

  1. Nov 3, 2012 #1
    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 [[itex]\frac{-b}{2}[/itex], [itex]\frac{b}{2}[/itex]], 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 [itex]\frac{1}{\pi}[/itex][itex]\intf(x)dx[/itex] definite integral from -π/2 to π/2.

    a1 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.

    b1 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 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. jcsd
  3. Nov 3, 2012 #2
    If a function is odd, can it have cosine terms?
    If a function is even, can it have sine terms?
     
  4. Nov 3, 2012 #3

    LCKurtz

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  5. Nov 3, 2012 #4
    Sorry, I didn't mean to repost. I was trying to change the red font and it reposted. Sorry.
     
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