Regions formed by polar coordinates in double integration.

Question

I need to sketch the region of integration of the following double integral in the $xy$ plane:

$$\int_0^{\pi/2}\int_0^{1/\cos\theta} f(r,\theta) \ dr \ d\theta,$$

where $f(r,\theta)= re^{-\frac12r^2}.$

Is it as simple as just converting the polar limits to cartesian ones and then sketching that or is there more to it?

Thanks!