- Purpose
- Getting Started
- Background
- Cardioids, Limaçons, and Roses
- Intersections of Curves in Polar Coordinates
- Area in Polar Coordinates

- Exercises

\\filer\calclab

when you hit enter, you can then choose MA1023 and then choose the worksheet

Polar_start_B11.mw

Remember to immediately save it in your own home directory. Once you've copied and saved the worksheet, read through the background on the internet and the background of the worksheet before starting the exercises.

The main reason for using polar coordinates is that they can be used to simply describe regions in the plane that would be very difficult to describe using Cartesian coordinates. For example, graphing the circle in Cartesian coordinates requires two functions - one for the upper half and one for the lower half. In polar coordinates, the same circle has the very simple representation .

Name | Equation |

cardioid | or |

limaçon | or |

rose | or |

- A point in the plane can have more than one representation in polar coordinates. For example, , is the same point as , . In general a point in the plane can have an infinite number of representations in polar coordinates, just by adding multiples of to . Even if you restrict a point in the plane can have several different representations.
- The origin is determined by . The angle can have any value.

>Area1:=1/2*int((1-cos(theta))^2, theta=0..2*Pi); >evalf(Area1);

- For each of the following polar equations, plot the graph in polar coordinates using the
`plot`command and identify the graph as a cardioid, limaçon, or rose. - Find all points of intersection for each pair of curves in polar
coordinates.
- and for .
- and for . Find the area inside and outside .

- Plot the polar equation . Find the angles that create the the inner loop of . Plot only the inner loop and then find the area inside the inner loop.

2011-11-03