Frequency spectrum of an amplitude modulated signal
With $s$, $m$, and $c$ as you display, then the diagram of $S(\omega)$ is incorrect.  If it were, the spectrum of $m$ would be a triangle centered at zero frequency, which it is not.

$$
S(\omega) = \frac{A_cA_m}{4} \left[\\
\delta\left(\omega - (\omega_c + \omega_m)\right)\\
+ \delta\left(\omega - (\omega_c - \omega_m)\right)\\
+ \delta\left(\omega - (-\omega_c - \omega_m)\right)\\
+ \delta\left(\omega - (-\omega_c + \omega_m)\right)\\
\right]$$