Multiplication of Sinusoids

What happens when we multiply a low frequency sinusoids with a higher frequency sinusoid?

It can be shown mathematically that

$$x(t) = \sin(2\pi(220)t)\cos(2\pi(2)t)$$

$$= \frac{1}{2}\left[\sin(2\pi(222)t)+\sin(2\pi(218)t)\right]$$

which is the sum of sine functions.

Notice the sinusoidal components in the spectrum are not the same frequency as the two multiplied sinusoids--rather, they are the sum and the difference.

Sinusoidal multiplication can therefore be expressed as addition (which makes sense because all signals can can be represented by the sum of sinusoids).