Exploring Sine Functions
Given the following function; y=a(sin(bx+c)), the value of ÒaÓ will affect the amplitude. The value of ÒbÓ will change the period and the value of ÒcÓ will alter the position that our function starts at on the x-axis. The original sine function below begins at x=0. Changing ÒcÓ will either move right or left depending on whether ÒcÓ 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 ÒaÓ 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 ÒbÓ 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 ÒbÓ is increased and decreased.