Assignment 10: Parametric Curves

Laura Dickerson

Let's look at these two equations x= cos (t) and y=sin (t) graphed as a parametric curve.

How can we change the equations to explore other graphs?

In the above graph, we have constructed the unit circle as a parametric curve. What if we instead want to construct a larger or even a smaller circle using parametric curves. This may be a great challenge for students to work on. What they will learn is that they will have to change the values of the x and y not the t. If we graph x = n cos t and y = n cos t, we will get circles varying in sizes.

 

 

 

 

 

 

Another change that we might want is to only look at part of the circle. The following equations will graph only part of the unit circle.

For a semicircle try:

For a quarter of a circle try:

For three-fourths of a circle try:

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