Through graphical means, investigate the effects of allowing the variable

This function is called the Cartioid.

Using Derive:

- Prepare the program for graphics.
- If the first menu item is
*Algebra*then press . - Press for
*Author*. - Enter the function
r = 1 + cos(0* +) - Press to get the plot window.
*Now we need to prepare Derive to graph in polar coordinates.* - Press to enter the options menu.
- Now press to enter the state menu.
- Finally, press and then
to tell Derive to graph using continuous polar coordinates.
**Note: Derive will continue to graph in polar coordinates for the remainder***of the session or until the state is chaged back to rectangular.*

- Now press and then to see the graph.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(.25* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- That graph appears as follows:

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(.5* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(.75* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(1* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(1.25* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(1.5* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(1.75* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r = 1 + cos(2* +) - Press to get the plot window.

*Derive will automatically redraw any old graphs; so don't be surprised when the old graph(s) appear.* - Now press and then
to see the new graph drawn.

- Now we have the following picture:

- The picture requires multiple equations, i.e. multiple values of a and b.
- If you need more help see Polar Coordinates - 2.
- This will help you learn how to use the a values.

This document was originally written by **Richard Rupp**.