Find the Third-Degree Fourier Polynomial For $f(t)=$ $\left\{\begin{array}{l}0 \\c\end{array}\right.$ $\begin{array}{c}-2 <\\0<\end{array}$

Multiple Choice

Find the third-degree Fourier polynomial for $f(t) =$$\left\{\begin{array}{l}0 \\c\end{array}\right.$$\begin{array}{c}-2 <\\0<\end{array}$$\begin{array}{l}x \leq 0 \\x \leq 2\end{array}$ , where c is a constant, by writing a new function, $g(x) =f(t)$ , with period $2 \pi$ .

A) $\frac{c}{2}-\frac{2 c}{\pi} \sin \left(\frac{\pi t}{2}\right) -\frac{2 c}{3 \pi} \sin \left(\frac{3 \pi t}{2}\right)$
B) $\frac{c}{2}+\frac{2 c}{\pi} \sin \left(\frac{\pi t}{2}\right) +\frac{2 c}{3 \pi} \sin \left(\frac{3 \pi t}{2}\right)$
C) $\frac{c}{2}+\frac{2 c}{\pi} \sin (t) +\frac{2 c}{3 \pi} \sin (3 t)$
D) $\frac{c}{2}-\frac{2 c}{\pi} \sin (t) -\frac{2 c}{3 \pi} \sin (3 t)$