# Thread: Fourier Cosine series of cos(x)

1. ## Fourier Cosine series of cos(x)

Hello peoples,

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

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

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

is all that happens as is that the cosine Fourier series of cos(x) goes to 0?

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

Cheers!

Sarah

2. Originally Posted by sarahisme
Hello peoples,

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

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

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

is all that happens as is that the cosine Fourier series of cos(x) goes to 0?

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

Cheers!

Sarah
Look at the limit of the coefficient of cos(pi x /alpha) as alpha goes to
pi.

You should find that the limit as alpha goes to pi of all the coeficients
other than that of cos(pi x /alpha) are 0, while that of cos(pi x /alpha)
is 1.

RonL

3. Originally Posted by CaptainBlack
Look at the limit of the coefficient of cos(pi x /alpha) as alpha goes to
pi.

You should find that the limit as alpha goes to pi of all the coeficients
other than that of cos(pi x /alpha) are 0, while that of cos(pi x /alpha)
is 1.

RonL
i yep i see, i need to be more careful with the n = 1 term when alpha = pi.

thanks for the help!