By: Melissa Wilson

In this assignment we will examine what happens when the a, b, and c parameters in the equation below are varied. We will examine each parameter individually.

First, let's look at the

aparameter. Shown below, I vary theaparameter from 1 to 5.Observations:

- As the
aparameter increases, the amplitude of the sine wave increases. Sinceais outside of the sine function it serves to multiply the value of sine at each x-value.- You can also see that the places where the sine curve cross the x-axis remains the same regardless of what the parameter is changed to. This indicates the period for each sine equation is independent of the
aparameter.Now, let's compare positive and negative parameters. As you can see, a negative

aparameter makes the sine curve reflected over the x-axis.

Now, let's examine the parameter

b. We will vary thebparameter and see what happens as we increase the value and then also compare negative and positive values.Observations:

- As
bincreases the period of the sine wave decreases.- The amplitude of the sine wave does not change as in the previous example with the
aparameter.

Below are the equations used to examine the effects of negative and positive parameters. The resulting graph is shown below. Similarly to how the

aparameter was effected by the negative value, thebparameter being negative will cause the sine wave to be reflected across the x-axis.

Finally, let's vary the

cparameter. First we will take increasing values forc. Changing thecparameter shifts the entire sine curve horizontally. The period and amplitude for the sine curve does not change.Observe that the negative values for

c(as shown below) also have the same effect as the positive effects (only in the negative x-direction)