We have plotted *y *= 2 cos 2*x* (light blue) and *y *= 3 sin *x* (dotted light green) so you can see where the composite graph comes from.

**Note 1: **You will notice in this last example that there is a regular pattern forming. In fact, it is a simple example of a Fourier Series, which we meet (much) later in the Advanced Calculus section.

**Note 2: **Of course, we will mostly use the computer to graph these composite graphs. It is often very tedious to add many *y*-values in a table. However, the important thing is to understand that a composite graph is the **sum** of the *y*-values of two (or more) graphs. Or, we can have products (and quotients) of functions that will also give us composite trigonometric graphs.