Finding a2 in a Fourier Series

andre_1
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Homework Statement



Find the term a2 in the following Fourier seies:


[4+5 (cos x )^2]^(1/2) dx= ao + a2 cos (2x) + a4 cos (4x)

The Attempt at a Solution


The only thing I can think about is transforming that to complex numbers but I am not completely sure...

I know that a0 is supposed to be 3.966360

Thanks!
 
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Is that an integral on the left side? Are you asked to write
\int\sqrt{4+ 5 cos^2(x)} dx
as a Fourier series?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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