# 3d polar plot

I have to do a 3d polar plot. i.e. I have to make a 3d plot by rotating a 2d polar plot along the vertical axis.

The polar plot is of the form r=f(theta). But the polar_plot function in sage gives me only 2d plot. How do I get a 3D version of it?

I tried spherical_plot but it is not giving me the plot which I expect to be equivalent to the revolution surface I get from rotating the 2d polar plot along vertical axis.

Example:

```
show(polar_plot(sin(2*theta),theta,0,2*pi))
```

I wanted to plot this `sin(2*theta)`

function as a 3d plot, by revolving it around by it's vertical axis.
But the command

```
spherical_plot3d(sin(2*theta),(theta,0,2*pi),(x,0,pi))
```

Is not giving me that. It is giving me another shape instead.

Or Another Example: polar_plot of cos(theta)

I want to do a 3d polar plot of this to get a doughnut shape

I shall also give another example with pictures. The following plot is what I wanted using spherical3d plot

But in sage, giving the same command is giving me this plot instead.

What command should I give in sage to get a plot like the one we get from Mathematica?

I have added example.