Exploring Sine Functions

Erin Mueller

Given the following function; y=a(sin(bx+c)), the value of “a” will affect the amplitude. The value of “b” will change the period and the value of “c” will alter the position that our function starts at on the x-axis. The original sine function below begins at x=0. Changing “c” will either move right or left depending on whether “c” is positive or negative.

Above, we can see the graph of a regular sine graph. However, watch what happens when we change certain characteristics to the sine graph. When we change the value of “a” in y=a(sin(x)), we will change the amplitude. The amplitude represents the maximum value for which the sine graph will reach on the y-axis before it begins to descend. The amplitude for the original sine function is 1.

When we alter the value of “b” in our y=a(sin(bx+c)) function, the period changes. The period of the original sine function is 2. This means that after x=2, the graph will begin to repeat itself. From the graphs below, we can observe what happens when the value of “b” is increased and decreased.