Graphs of y = a sin bx and y = a cos bx

The b in both of the graph types
y = a sin bx
y = a cos bx
affects the period (or wavelength) of the graph. The period is the distance (or time) that it takes for the sine or cosine curve to begin repeating again.
The period is given by:

Note: As b gets larger, the period decreases.

Changing the Period

First, let's look at the graph of y = 10 cos x, which we learned about in the last section, sine and cosine curves.

As we learned, the period is 2π.
Now let's look at y = 10 cos 3x. Note the 3 inside the cosine term.

Notice that the period is different. (The amplitude is 10 in each example.)
This time the curve starts to repeat itself at x = 2π/3. This is consistent with the formula we met above:

Now let's view the 2 curves on the same set of axes. Note that both graphs have an amplitude of 10 units, but their period is different.