Let $\displaystyle f(x) = \begin{cases} 0\quad & \text{for}\ \ 0 < x < 1, \\ -\left(4-x\right)\quad & \text{for}\ \ 1 < x < 4. \end{cases}$

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$\bullet\quad$ Compute the Fourier sine coefficients for $f(x)$.

• $B_n =$

$\bullet\quad$ Give values for the Fourier sine series $\displaystyle S(x) = \sum_{n=1}^\infty B_n\,\sin\left(\frac{n\pi}{4}\,x\right)$.

• $\phantom{-}S(1) =$
  
  
• $S(-2) =$
  
  
• $\phantom{-}S(5) =$