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

Changing the value of **c** caused the graph to slide horizontally
along the x-axis. When **c** = 1, the graph moved a distance
of -1 along the x-axis. When **c** = 3, the graph moved a distance
of -3 along the x-axis. When **c** = -2, the graph moved a
distance of 2 along the x-axis. And when **c** = -5, the graph
moved a distance of 5 along the x-axis. This movement can be seen
by comparing the x-intercepts on the various graphs to the x-intercepts
of the first graph, y = sin x.

It appears that for any **c**, the graph will slide a distance
of - **c** along the x-axis.

It is important to point out that in this case neither the
amplitude nor the period was changed by different values of **c**.
The effect of **c** on the equation is to change the value
of x before any other function is performed. The result is a horizontal
shift of the graph.

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