Finding a Fourier Series: What to Do and How?

[Luongo]

1. We are supposed to find a Fourier series knowing only f(t)= acos(kt)+bcos(kt)
and some values of Fourier coefficients...

please see #2 on this link http://www.math.ubc.ca/~oyilmaz/courses/m267/hmk3.pdf
2. I am using c_k=1/2pi $$\intf(t)e^-ikt$$dt
3. are we supposed to convert f(t) into expnential form? i got 4 different expos thus 4 integrations, i have no idea which method i should solve it...

 

[LCKurtz]

You only have 5 nonzero coefficients. Write out the 5 term complex series and then change it to a sine-cosine series using e^iθ = cos(θ) + i sin(θ) and collecting terms.