Consider the following three continuous$-$time signals with a fundamental period of T $=112$: x$($t$)=$ cos$(41$Tt$),$ y$($t$)=$ sin$(47$Tt$),$ z$($t$)=$ x$($t$)$y$($t$).($a$)$ Determine the Fourier series coefficients of x$($t$).($b$)$ Determine the Fourier series coefficients of y$($t$).($c$)$ Use the results of parts $($a$)$ and $($b$),$ along with the multiplication property of the continuous$-$time Fourier series, to determine the Fourier series coefficients of z$($t$)=$ x$($t$)$y$($t$).($d$)$ Determine the Fourier series coefficients of z$($t$)$ through direct expansion of z$($t$)$ in trigonometric form, and compare your result with that of part $($c$).$