Hello, this question is about symmetry of polar coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

For a polar-curve to be symmetric around the x-axis we require that if (r,a) lies on the graph then (r,-a) or (-r,Pi-a) lies on the graph.

To be symmetric about the y-axis we require that (-r,-a) or (r,Pi-a) lies on the graph.

Now lets look at the graph r=cos(a/2)

Since cos(-a/2)=cos(a/2) then the curve is symmetric about the x-axis. Of the requirements of symmetri I wrote earlier it doesn't seem to be symmetric about the y-axis. But when I draw it, symmetry about the y-axis occours. How can this be shown mathematically?

hyper

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# Very hard question about polar coordinates

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