Project 9: Parametric & Polar Equations

Instructions

Use Maxima to work this project. Each group should email an annotated Maxima file to the instructor.

Polar Functions

What to do

Create a gallery of polar graphs. For each of function, find the following items.

1. Graph the function
2. Find the length of the curve
3. Find the area enclosed by the curve, unless otherwise indicated

Be sure to pay attention to domain.

Functions to use

Here are the curves to use.

1. The circle \( r = 4 \)
2. The odd petaled rose \( r = 4 \cos 3\theta \)
3. The even petaled rose \( r = 3 \cos 4\theta \)
4. The dimpled limaçon \( r = 4 +3\sin \theta \)
5. The cardiod \( r = 5 - 5 \cos \theta \)
6. The convex limaçon \( r = 5 - 2\sin \theta \)
7. The limaçon with an inner loop \( r = 3 + 4 \cos \theta \); just find the area inside the loop
8. The lemniscate \( r^2 = 9 \sin 2\theta \)
9. The burst \( r = 5 + \sin (12 \theta ) \)