(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the fourier series f(x) = [tex]\sum[/tex]a_{n}sin(nx) + b_{n}cos(nx) can be written as [tex]\sum[/tex]k_{n}(cos(nx+[tex]\vartheta[/tex])) and define k_{n}and [tex]\vartheta[/tex]

where the summation is from 0 to [tex]\infty[/tex]

2. Relevant equations

sin [tex]\vartheta[/tex] = cos (90 - [tex]\vartheta[/tex]) ??

3. The attempt at a solution

Well what I originally did was replace the sin term by cos (90 - nx), put cosine in terms of complex exponentials, and then try to solve the equation, but I only got what I was given in the first place and not the solution (i.e. I went in a circle).

Is there some kind of property of sin or cos I could use?

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# Homework Help: Fourier Series

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