What do you know about "spherical coordinates"? In standard spherical coordinates, we have , the straight line distance from the origin to the point, , the angle a line from the origin to the point on the xy-plane directly below the given point makes with the x-axis (the same angle as in two-dimensional polar coordinates, and [itex]\phi[/itex] the line from the origin to the point makes with the xy-plane. You can think of the two angles as being "longitude" and "co-latitude" (since it is measured from the "north pole" rather than the "equator").
In spherical coordinates, , , and .
Here, I notice we have "sin" in z rather than "cos". Okay, they are using "latitude" rather than "co-latitude". That is, they are using so that
Finally, note the changes in notation: r instead of , instead of , and instead of .