\text { Let } f:[0, \pi] \rightarrow \mathbf{R} \text { be given by } f(x)=\left\{\begin{array}{ll} -2-\sin (2 x) & \text { for } x \in\left[0, \frac{\pi}{2}\right) \\ 2 x-\pi &

\text { for } x \in\left[\frac{\pi}{2}, \pi\right) \\ 2 & \text { for } x=\pi \end{array}\right. \text { (a) For } x \in[-\pi, \pi] \text {, draw the graph of the Fourier sine series of } f(x) \text {. } \text { (b) For } x \in[-\pi, \pi] \text {, draw the graph of the Fourier cosine series of } f(x) \text {. } (c) Please explain, in words, how you know that your answer in (b) is indeed the graph of the Fourier cosine series.Fourier coefficients