$[20$ points$]$ In communications a low frequency "message" signal, $m(t),$ is boosted to high frequency by multiplying it by a high frequency "carrier" cosine, $c(t).$ This boosted signal may now be efficiently transmitted wirelessly. Answer the following related questions. Hint: use the tables at the end of the test.

a$.[5$ points$]$ If the message signal is $m(t)=Sa(2t)=\frac{sin(2t)}{2t}$ what is the frequency spectrum $($i$.$e$.,$ Fourier transform$)$ of this signal, denoted as $M()?$

b$.[5$ points$]$ If the carrier signal is $c(t)=cos(1000t)$ what is the frequency spectrum $($i$.$e$.,$ Fourier transform$)$ of this signal, denoted as $C()?$

c$.[10$ points$]$ If the product signal is given by $x(t)=m(t)c(t),$ what is the frequency spectrum $($i$.$e$.,$ Fourier transform$)$ of this product signal, denoted as $x()?$ Express your final answer in closed form with no convolution operators.

Make sure it is correct i need it soon