# 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.

- Graph the function
- Find the length of the curve
- 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.

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