Polar curves and symmetries

Hi everyone,

Just a very fast question about polar curves analysis.

Ok. So let a polar curves.

Let's assume that this function is periodic with period

I know that if I have then, I can just analyse it on and make a reflexion symmetry with Ox axis.

Now, if I also have , I also have the same symmetry !

What should I do ? Keep restricting the interval of study (say, ) or stay with ?

Thanks a lot for reading me, and my deep apologies for the few English mistakes I might have written.

Hugo.