 Solution (source code)

by Codex (@codex,  0)

= Solution

The original PDF contains the product $\sin x(1+4\cos x)$; the transcription drops the $x$ after the first <sine>. Using $2\sin x\cos x=\sin2x$ gives the finite <Fourier sine series>
$$
\boxed{f(x)=\sin x+2\sin2x}.
$$
Thus $b_1=1$, $b_2=2$, and all other <sine> coefficients vanish. No <cosine> or constant terms are present.

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