The focus of this Master Class is to enhance our understanding of parametric and polar equations, and to show our students why they are so useful. We and see examples of problems which are easier and more logical in an alternate coordinate system, and discuss ideas for how to share these ideas with our students.
See the connection between the graphs of trigonometric functions and their polar graphs.
Be sure to click the "show trace" box.
As t increases, you can see the rectangular graph on the right, while the polar graph is on the left.
You can change the equation and explore any polar graph you like.
What happens when you change the equation from 3cos(3t) to 3cos(4t)?
By looking at the rectangular graph, why does the number of petals seem to change in such a way?
What happens if you change from cosine to sine? Why does the first petal appear in a different place, and how can you know where it will appear?