Area of a Circle in an Electron's Hydrogen Atom

[Anthill]

TL;DR Summary

What does the shape that has, in polar coordinates, a given surface area look like?

My textbook says "A is the area of the circle enclosed by the current" (produced by an electron in a hydrogen atom), A = $\pi r^2 \sin(\theta)^2$. I don't understand where the $\sin(\theta)^2$ comes from.

 

[Mark44]

Summary:: What does the shape that has, in polar coordinates, a given surface area look like?

My textbook says "A is the area of the circle enclosed by the current" (produced by an electron in a hydrogen atom), A = $\pi r^2 \sin(\theta)^2$. I don't understand where the $\sin(\theta)^2$ comes from.

Assuming that the radius of the circle is x, the area would be $A = \pi x^2$.

Converting to polar coordinates, $x = r \sin(\theta)$, so $x^2 = r^2 \sin^2(\theta)$, and the area would be $\pi r^2\sin^2(\theta)$.
Note that powers of trig functions are usually denoted like this: $\sin^2(\theta)$ rather than this $\sin(\theta)^2$.