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# Fourier Coefficients by Inspection... HELP!! watch

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1. I need help on the following questions. I have absolutely no idea how to do this, from working out the period to finding the Fourier coefficient.

For each question I need to state the period and by just looking at the function, work out its Fourier coefficients.
1) f(x) = 1 + cos(2pix) + sin(4pix)

2) f(x) = 1 + cos^2(2pix) - cos(4pix). Hint: use 2cos^2(x) = 1 + cos(2x)

If anyone can help it would be much appreciated.
Thanks
2. The easiest way to find the period would be to graph the functions and look at how often they repeat. If you need to show it formally, use the fact that f(x+k) = f(x) for all x if f has period k, so set up and solve f(x+k)=f(x) (I havent tried it, it looks like it would fall out easily with the double angle formulae).
3. Any ideas on how to get the Fourier coefficient?

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Updated: March 11, 2008
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