Fourier Trigonometric Series for Symmetric Function: Homework Check

roldy
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Homework Statement


Determine the first three terms in the Fourier trigonometric series for the function shown below.


Homework Equations


Look at attached jpeg. This tex tool is terrible. After making correction to the code, the preview still shows previous preview posts.


The Attempt at a Solution



See attached jpeg for solution and the other attachment for the function. Did I define the function correctly? I didn't solve for bn because this function is symmetric about the y-axis.

First three terms mean a0, a1, and a2 right?
Or is it n=1, 2, 3
 

Attachments

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  • Untitled-1.jpg
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Would anyone check this for me please?
 

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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