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?
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.