Thanks Valeriu,
Actually I was able to get the result I was looking for with:
RevolutionPlot3D[{(Sqrt[Cos[2*\[Theta]]])*Sin[t], t}, {t, 0, 2 Pi}, {\[Theta], -Pi/4, Pi/4}]`
This is the exact same code as Maple10 plot3d cylindrical coordinates, so perhaps RevolutionPlot3D could be called cylindrical coordinates.
