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.

Observations:

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.

Observations:

 

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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