I set **a**=1 and **c**=0, which gave the equation y
= sin bx. I then tried different values for **b** and graphed
the results. Some examples follow.

Changing the value of **b** affected the period of the equation.
It basically stretched or shrank the graph horizontally. For **b**
= 2, the period was changed by a factor of 1/2. For **b** =
4, the period was changed by a factor of 1/4. For **b** = -2,
the period was changed by a factor of 1/2 and the graph was reflected
about the x-axis. For **b** = -4, the period was changed by
a factor of 1/4 and again the graph was reflected about the x-axis.

It appears that for any **b**, the period is changed by
a factor of 1/**b**. In addition, for negative values of **b**,
the graph is reflected about the x-axis.

It is important to point out that the graph continued to pass
through the point (0,0) regardless of how **b** was changed.
When x = 0, it does not matter what the value of **b** is since
bx will always equal 0. The result is that when x = 0, sin bx
= sin x for any value of **b**. Therefore, the graph will always
pass through the origin.

Click **here** to see
an animated graph of this equation.