# 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:

• As the a parameter increases, the amplitude of the sine wave increases. Since a is 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 a parameter.

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:

• As b increases the period of the sine wave decreases.
• The amplitude of the sine wave does not change as in the previous example with the a parameter.

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)