Use graphing to determine the effects of changing the a and b values in the following polar equation:

Using Derive:

- Prepare the program for graphics.
- If the first menu item is
*Algebra*then press . - Press for
*Author*. - Enter the function
r=sin - 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=.5 sin - 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=2 sin - 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=3 sin - 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.

- At this point our graph will be like the following:

- At this point our graph will be like the following:

- First we have to clear the plot window by pressing and then
- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r=3 sin - 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.

- As expected from before, the graph looks like the following:

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r=3 sin (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.

- Next press to return to the algebra window.
- Press for
*Author*. - Enter the function
r=3 sin (4) - 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=3 sin (8) - 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.

- At this point our graph will be like the following:

- At this point our graph will be like the following:

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