## Graphs: Special Trigonometric Functions

A pure tone, such as one produced by a tuning fork, is a wave form that looks like a sine curve. Sounds in general are more than just simple sine waves. They are combinations of sine waves and other functions. A vibrating string on a violin or fiddle is made up of a combination of several sine waves. The resulting wave form can be found by adding the ordinates of the respective sine waves. This can easily be seen if all the component wave forms are graphed on the same set of axes. Figures , , and show the resulting wave form when two component wave forms are added together.

**Example 1:** Graph the functions *y* = *x* and *y* = 4 sin *x* on the same coordinates and graph their sum.

**Figure 1**

Drawing for Example 1.

**Example 2:** Graph the functions *y* = *x*/2 and *y* = 4 sin *x* on the same coordinates and graph their sum.

**Figure 2**

Drawing for Example 2.

**Example 3:** Graph the functions *y* = 10 sin *x* and *y* = 4 sin 3 *x* on the same coordinates and graph their sum.

**Figure 3**

Drawing for Example 3.