Question 631549
r = 3 - 6 cos theta
<pre>
r is a relative minimum when cos(@) is a relative maximum

cos@ is an absolute and a relative maximum of 1 when @ = 0,  

therefore r is a relative minimum when @ = 0, r = 3 - 6(1) = -3

So we plot the polar point (-3,0) [which is the rectangular point (-3,0)]

That is the end of the inner loop.

r is a relative maximum when cos(@) is a relative minimum

cos@ is an absolute and relative minimum of -1 when @ = pi, therefore 

r is a relative maximum when @ = pi, r = 3 - 6(-1) = 9

So we plot (9,pi), [which is the rectangular point (-9,0)] 

That is the end of the outer loop.

The y-intercepts are found when @ = pi/2 a,d 3pi/2

r = 3 - 6 cos(pi/2) 
r = 3 - 6·0
r = 3    

So they are the polar point (3,pi/2) and (3,3pi/2)

which are the rectangular points (0,3) amd (0,-3)

The graph is like this:

{{{drawing(400,400,-10,4,-7,7,graph(400,400,-10,4,-7,7),

circle(-9,0,.1), circle(-.4,.51,.1),circle(-.88,.88,.1),circle(-1.4,1.07,.1),
circle(-1.9,1.1,.1),circle(-2.3,.97,.1),circle(-2.7,.72,.1),circle(-2.9,.38,.1),
circle(-3,0,.1),circle(-2.9,-.38,.1),circle(-2.7,-.72,.1),circle(-2.34,-.97,.1),
circle(-1.9,-1.1,.1),circle(-1.4,-1.07,.1),circle(-.88,-.88,.1),circle(-.4,-.52,.1),
circle(0,0,.1), circle(.27,.54,.1),circle(.37,1.4,.1),circle(.29,2.2,.1),
circle(0,3,.1),circle(-2.3,.97,.1),circle(-2.7,.72,.1),circle(-2.9,.38,.1),
circle(-3,0,.1),circle(-.49,3.75,.1),circle(-1.18,4.4,.1),circle(-2.03,4.89,.1),
circle(-3,5.2,.1),circle(-4.05,5.28,.1),circle(-5.12,5.12,.1),circle(-6.16,4.72,.1),circle(-7.1,4.1,.1),circle(-7.89,3.27,.1),circle(-8.5,2.28,.1),circle(-8.87,1.17,.1),

circle(0,0,.1), circle(.27,-.54,.1),circle(.37,-1.4,.1),circle(.29,-2.2,.1),
circle(0,-3,.1),circle(-2.3,-.97,.1),circle(-2.7,-.72,.1),circle(-2.9,-.38,.1),
circle(-3,0,.1),circle(-.49,-3.75,.1),circle(-1.18,-4.4,.1),circle(-2.03,-4.89,.1),
circle(-3,-5.2,.1),circle(-4.05,-5.28,.1),circle(-5.12,-5.12,.1),circle(-6.16,-4.72,.1),circle(-7.1,-4.1,.1),circle(-7.89,-3.27,.1),circle(-8.5,-2.28,.1),circle(-8.87,-1.17,.1)


   )}}}

Edwin</pre>