Question

how do I test symmetry to the polar axis of r= 3-3cos(Ɵ)

Answer 1

-symmetry to the x-axis,test if r(theta) = r(-theta)
in this case: 3-3cos(theta) =3-3cos(-theta) [cos(theta)=cos(-theta)], so the graph has x-axis symmetry
-to the y-axis, test if r(theta) =r(pi-theta)
3-3cos(theta)= 3-3cos(pi-theta)?
-to the origin, test if r(theta)= r(pi+theta)