Rotationally speaking, the bug starts on the y-axis at 10 cm ( ) and spins for 2 min. The angular speed is constant, so
So in cylindrical coordinates the bug is at
after 2 minutes.
In rectangular coordinates we have
Using rectangular coordinates as the starting point, we have for spherical coordinates:
<-- Not the same as before!
Now, would normally be but since x is 0 this cannot be calculated directly. Suffice it to say that needs to be such that is positive and infinite. Thus . (The other way to see this is that in spherical coordinates is the same as in cylindrical coordinates.)
(As far as I know there is no exact expression of this.)
So in spherical coordinates we have: