Fourier Series Integral Identities

For the Forier series whose Period is 2 and f(t) = cos( pie/2 * t)

I have trouble getting the trig identity down.
eventually I reach a_0 = 4 / pie
but once I come to a_n
I cannot understand how to integrate

the integral of [ cos(nt) * cos(pie /2 * t) * dt] from -1 to 1

I have tried integration by parts but to no avail


Thank you for your time
 

Chris L T521

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May 2008
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For the Forier series whose Period is 2 and f(t) = cos( pie/2 * t)

I have trouble getting the trig identity down.
eventually I reach a_0 = 4 / pie
but once I come to a_n
I cannot understand how to integrate

the integral of [ cos(nt) * cos(pie /2 * t) * dt] from -1 to 1

I have tried integration by parts but to no avail


Thank you for your time
Recall that \(\displaystyle \cos\alpha\cos\beta=\tfrac{1}{2}\left[\cos(\alpha+\beta)+\cos(\alpha-\beta)\right]\). In your case, let \(\displaystyle \alpha=nt\) and \(\displaystyle \beta=\tfrac{1}{2}\pi t\).

Can you proceed?