How to calculate the Fourier series of $\sin x-4\sin 3x+7$

71 Views Asked by Bumbble Comm At 24 Apr 2026 - 9:31

I obtain $0$ por the an and bn coeficients, and I think that's incorrect...

There are 1 best solutions below

Bumbble Comm On 03 Mar 2016 - 9:24

As Matt Samuel said in a comment, the function is already in the Fourier series form. Recall that your goal is to write the function $f(x)$ as

$$ f(x) = a_0 + a_1\cos x + b_1 \sin x + a_2\cos 2x + b_2 \sin 2x + a_3\cos 3x + b_3 \sin 3x + \cdots $$

Can you see why your function is already in this form? Can you see the only 3 coefficients that are not zero?