# Fourier Cosine series of cos(x)

#### sarahisme

Hello peoples,

I think this is a trick question... well sort of :P

http://img133.imageshack.us/img133/472/picture8ox1.png [Broken]

for part (a) i get that the cosine Fourier Series for f(x) = cos(x) to be:

http://img138.imageshack.us/img138/6114/picture9sq2.png [Broken]

i hope that is ok, but its part (b) that is troubling me...

is all that happens as http://img138.imageshack.us/img138/7436/picture10gf7.png [Broken] is that the cosine Fourier series of cos(x) goes to 0?

i am guessing i am missing some trick to this question?

Cheers! :D

Sarah

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#### jpr0

When you let $\alpha\to\pi$ then the interval you're computing the fourier series on becomes $[-\pi,\pi]$. The original function you're given, $\cos(x)$ is exactly periodic on this interval, and so you should find that your fourier series has only coefficient, for $n=1$, which corresponds to $cos(x)$.

#### sarahisme

jpr0 said:
When you let $\alpha\to\pi$ then the interval you're computing the fourier series on becomes $[-\pi,\pi]$. The original function you're given, $\cos(x)$ is exactly periodic on this interval, and so you should find that your fourier series has only coefficient, for $n=1$, which corresponds to $cos(x)$.
ah yep i see now. i need to be more careful with the n = 1 term when alpha = pi

thanks for the help! :D

Sarah

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