Question $1(30$ points$)$: FS

We are given two periodic signals given in Fig. $1.$

Figure $1$: Two periodic signals for Q$.1$

$($a$)(10$ Pts$.)$ Determine the Fourier Series $($FS$)$ coefficients for $\backslash ($ x$\_\{1\}($t$)\backslash ).$

$($b$)(10$ Pts$.)$ Determine the Fourier Series $($FS$)$ coefficients for $\backslash ($ x$\_\{2\}($t$)\backslash ).$

$($c$)(10$ Pts$.)$ What is the relationship between the FS coefficients of the two signals? Mathematically prove and verify with your results from Parts $($a$)$ and $($b$).$

c$1=4$ c$2=7$ c$3=-1$ c$4=11$ c$5=6$