# Polar curves and symmetries

• May 16th 2011, 12:14 PM
Hugal
Polar curves and symmetries
Hi everyone,

Just a very fast question about polar curves analysis.
Ok. So let $\rho= f(\theta )$ a polar curves.
Let's assume that this function is periodic with period $2 \pi$
I know that if I have $\rho ( - \theta ) =\rho (\theta)$ then, I can just analyse it on $[0, \pi]$ and make a reflexion symmetry with Ox axis.

Now, if I also have $\rho ( \pi - \theta) = - \rho (\theta)$, I also have the same symmetry !
What should I do ? Keep restricting the interval of study (say, $[0, \frac{\pi}{2}]$) or stay with $[0,\pi]$ ?

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

Hugo.