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alias99

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## Homework Statement

Find the Fourier cosine series for f(x) = cos x, 0 < x < Pi

**EDIT:**I believe we are talking about a half-range extension..

## Homework Equations

Fourier cosine series:

f(x) = a

_{0}/2 + Sum(n = 1 to infinity) (a

_{n}* cos (nx))

where a

_{0}= 2/L * integral (x = 0, x = L) (f(x) dx)

and a

_{n}= 2/L * integral (x = 0, x = L) (f(x) * cos (n*Pi*x/L) dx)

Sorry if thats hard to understand...

## The Attempt at a Solution

I graphed the function and extended the period to - Pi, i.e. -Pi < x < Pi

I found a

_{0}= 2/Pi * integral (x = 0, x = L) (cos x dx) = 0

a

_{n}= 2/Pi * integral (x = 0, x = L) (cos x * cos (nx) dx)

and evaluated the integral using IBP...

a

_{n}= 2/Pi * (ncos(x)*sin (nx) - sin(x)cos(nx))*1/(n

^{2}-1)| x = 0, x = Pi

which gives me a

_{n}= 0!

So the Fourier cosine series would be:

f(x) = 0

I would really appreciate any clarification as getting 0 for the series doesnt sound right..

Thank you in advance

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