Ja, ich hab es nicht ganz verstanden gehabt. Mein neuer Ansatz wäre dieser hier...
a₀ = (1/π) * ∫[0, π] sin(x) dx = (1/π) * [-cos(x)]|[0, π] = (1/π) * (-cos(π) - (-cos(0))) = 2/π
aₙ = (1/π) * ∫[0, π] sin(x) * cos(nωx) dx = (1/π) * ∫[0, π] (1/2) * (sin((1 + n)ωx) + sin((1 - n)ωx)) dx
a₁ = (1/π) * ∫[0, π] (1/2) * (sin(2πx) + sin(0)) dx = (1/π) * ∫[0, π] (1/2) * (0 + sin(0)) dx = 1/2
aₙ = 0 (für alle anderen n)
bₙ = (1/π) * ∫[0, π] sin(x) * sin(nωx) dx = (1/π) * ∫[0, π] (1/2) * (cos((1 - n)ωx) - cos((1 + n)ωx)) dx
bₙ = 2/π (für alle ungeraden n)