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Rho= Sqrt[x^2 + y^2]; Theta= ArcTan[y/x]; Plot3D[z = (Sin[Theta] + Cos[Theta])*BesselJ[1, Rho], {x, -10,  10}, {y, -10, 10}]

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RevolutionPlot3D[(Sin[t] + Cos[t])*BesselJ[1, r], {r, 0, 10}, {t, 0, 2 Pi}]

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Rho = Sqrt[x^2 + y^2]; Theta = If[x y > 0, ArcTan[x, y], 2 Pi + ArcTan[x, y]];
Plot3D[(Sin[Theta] + Cos[Theta])*BesselJ[1, Rho], {x, -10, 10}, {y, -10, 10}]
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