Originally Posted by

**Redding1234** For the way I set it up, how could I figure out if $\displaystyle t$ 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:

$\displaystyle x = 1 + \cos \theta, y = \sin \theta, z = 2 \sin \frac{\theta}{2}, \theta = 0 \to 2 \pi$

If I try to solve for z using $\displaystyle x = 1 - \cos \theta, y = \sin \theta$, then I get to $\displaystyle z = 2\sqrt{\frac{1 + \cos \theta}{2}}$, and I cannot use a half-angle formula.

But if I solve for z using $\displaystyle x = 1 + \cos \theta, y = \sin \theta$, I get $\displaystyle z = 2 \sin \frac{\theta}{2}$ 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 $\displaystyle y = \sin \theta$ and then go from there.

Also, with that set up, it seems obvious enough that $\displaystyle 0 < \theta < 2 \pi$, but how can you tell which way to go? That's probably the toughest part of this type of problem for me.