# Fourier Series Integral Identities

#### stressedengineeringstuden

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

#### Chris L T521

MHF Hall of Fame
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

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 $$\displaystyle \beta=\tfrac{1}{2}\pi t$$.