$)$ Consider a periodic signal x$($t$)$ with fundamental frequency $$ and coefficients a$0=1$ a$1=2$ a$2=1$ a$-1=2$ a$-2=1$ a$)(5$ pts$)$ Write x$($t$)$ as a function of sin$()$ and$/$or cos$().$ b$)$ If y$($t$)=8$ cos$($t $)+2$ cos$(3$t $)$ i$)(5$ pts$)$ Find the period of z$($t$)=$ x$($t$)$y$($t$)($Explain why $!)$ ii$)(10$ pts$)$ Find the coefficients zk of z$($t$)=$ x$($t$)$y$($t$)$ by using the multiplication property of continuous time Fourier Series.