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

[mundane]

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

Homework Statement

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

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?

 

[aralbrec]

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

 

[LCKurtz]

This thread appears to be a duplicate of
https://www.physicsforums.com/showthread.php?t=649374

 

[mundane]

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