Assignment One: Exploring the Sine Wave

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 a parameter. Shown below, I vary the a parameter from 1 to 5.


Now, let's compare positive and negative parameters. As you can see, a negative a parameter makes the sine curve reflected over the x-axis.

Now, let's examine the parameter b. We will vary the b parameter and see what happens as we increase the value and then also compare negative and positive values.



Below are the equations used to examine the effects of negative and positive parameters. The resulting graph is shown below. Similarly to how the a parameter was effected by the negative value, the b parameter being negative will cause the sine wave to be reflected across the x-axis.

Finally, let's vary the c parameter. First we will take increasing values for c. Changing the c parameter 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)


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