MATH 164, Spring 2001        Due Date:
Name(s):
Extra Project 11.4b: Limacons
Objective
To investigate limacons whose equations are of the form r = 1 + c cos 9.
Narrative
If you have not already done so, read Section 11.4 of the text. In particular, be sure to read about limacons in Example 11 on p. 701 of the text. In that example, the author discusses limacons with equations of the form r = 1 + c siné*. In this project we investigate limacons with equations of the form r = 1 + ccosß.
Tasks
1. a) Type the command lines below into Maple in the order in which they are listed.  These commands plot the limacons whose polar coordinate equations are of the form r = 1 + ccos 9 for c = 0,0.5,1, 2.
#	Pro^	ect	11	4b:	Limacons
>	restart;				
>	rO	= t	->	1+0	0*cos(t);
>	rl	= t	->	1+0	5*cos(t);
>	r2	= t	->	1+1	0*cos(t);
>	r3	= t	->	1+2	0*cos(t);
>  plot({[r0(t),t,t=0..2*Pi],[rl(t),t,t=0..2*Pi],[r2(t),t,t=0..2*Pi], [r3(t),t,t=0..2*Pi]},coords=polar,scaling=constrained);
b) Continue by typing the command lines below into Maple in the order in which they are listed. These commands plot the limacons whose polar coordinate equations are of the form r = 1 + c cos 9 for c = 0,-0.5,-1,-2.
>   rO
>  rl
>  r2
>  r3
= t -> l-0.0*cos(t) = t -> l-0.5*cos(t) = t -> l-1.0*cos(t) = t  ->  l-2.0*cos(t)
>  plot({[r0(t),t,t=0..2*Pi],[rl(t),t,t=0..2*Pi],[r2(t),t,t=0..2*Pi], [r3(t),t,t=0..2*Pi]},coords=polar,scaling=constrained);
At this time, make a hard-copy of your typed input and Maple's responses. Then, ...
2. a) Label each graph you plotted in part (a) of Task 1 with its constant c by hand: label the graph of r = 1 + 0.5 cos 9 by "r = 1 + 0.5 cos 6", for example.
b) Label each graph you plotted in part (b) of Task 1 with its constant c by hand: label the graph of r = 1 — 0.5 cos 9 by "r = 1 — 0.5 cos 6", for example.