I am trying to graph r^2=2cos(2theta)

in my answer key it's supposed to be an infinity symbol but I get a 4 leaf lemniscate. I am in polar mode so what can be the error?

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- Mar 31st 2009, 01:03 PMaaronbCalculator help
I am trying to graph r^2=2cos(2theta)

in my answer key it's supposed to be an infinity symbol but I get a 4 leaf lemniscate. I am in polar mode so what can be the error? - Mar 31st 2009, 01:12 PMOpalg
If $\displaystyle \theta$ lies between $\displaystyle \pi/4$ and $\displaystyle 3\pi/4$ (or between $\displaystyle -3\pi/4$ and $\displaystyle -\pi/4$) then $\displaystyle \cos(2\theta)$ is negative and will not have a square root. So the top and bottom leaves of the lemniscate ought not to be there. Maybe you should rewrite the equation as $\displaystyle r = \sqrt{2\cos(2\theta)}$ and see what the calculator makes of that version.