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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.