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:



Edwin