Final answer:
The correct general formula for the coefficients bn of the Fourier sine series on the interval (0, π) is bn = 2/(nπ), given in option (a). This is the form of the coefficient before integration with the function Φ(x).
Step-by-step explanation:
The student has asked for the coefficients for the Fourier sine series of a function f(x) defined on the interval (0, π). To find the coefficients bn, we need to use the Fourier sine series formula, which is defined on the interval (0, L) by:
bn = Ø4/L ∣0L f(x) sin(nπx/L) dx
For a function defined on the interval (0, π), L = π, the coefficients formula simplifies to:
bn = Ø2/π ∣0π f(x) sin(nx) dx
The general formula does not yield a specific coefficient value without knowing the function f(x). However, if the student is seeking the general formula for bn coefficients of a Fourier sine series on the interval (0, π), option (a) bn = 2/(nπ) provides the correct form of the general coefficient before integrating the product of f(x) and the sine function.