Polar Equations #2
Directions: Use the computer program I See Graphs to complete each task.
Click the Polar Equations tab.
1) Use the mouse to enter the equation r = 1/(1 + sin(q)). Click Plot Graphs.
Describe the graph.
2) Clear the above graph and enter the equation r = 1/(0.5 + sin(q)). Click Plot Graphs.
Describe the graph.
3) Describe the graph of r = 1/(0.5 + cos(q)).
4) Sketch the graph of r = (1+sin(2q))/(1+cos(q)) to the right ..
We are used to sketching graphs from left-to-right. Polar graphs are often not plotted in that order. Click the 
button twice. Click Polar Options in the menubar at the top of the screen, then Autotrace. Watch as points are traced by the bug as q takes its values from its minimum to its maximum.
5) Sketch the graph of r = 1 + 2cos(q).
6) Sketch the graph of r = 1 - 2cos(q).
The shape of the graphs in 5 and 6 is limacon.
7) Sketch the graph of r =2 + 2cos(q).
When both constants are equal, the limacon is called a cardioid.
8) Sketch the graph of r = 3 + 2sin(q).
This limacon has no "loop" since the constant is greater than
the coefficient of the sine function.
9) Sketch the lemniscate defined by r 2 = cos(2q).
(Hint: plot the equation r = sqrt(cos(2q)) )