For the way I set it up, how could I figure out if

is going from 0 to 2 or from 2 to 0? Is a picture necessary? I was having trouble drawing and labeling a picture of the curve.

Do you mean:

If I try to solve for z using

, then I get to

, and I cannot use a half-angle formula.

But if I solve for z using

, I get

as you got.

That is a very helpful setup, but I have to wonder how you came up with that parametrization. I don't know how I could get such an answer without getting lucky enough to think to let

and then go from there.

Also, with that set up, it seems obvious enough that

, but how can you tell which way to go? That's probably the toughest part of this type of problem for me.