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

composite trigo graph

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.