Eliminating the parameter when sin and cos are involved.

Hello! I've just started Calculus in college but my Trig class in high-school was a joke and I didn't get much out of it (mostly my fault) so I thought this question would belong in the pre-university trig forum. Please correct me if I'm wrong.

a) Eliminate the parameter to find a Cartesian equation of the curve.

x = sin1/2theta , y = cos1/2theta , -pi <= theta <= pi

(sorry I'm also a noob on writing math nicely on a computer, a link to a tutorial would be nice)

I thought about using the rule of sin^2theta + cos^2theta = 1 but I'm not sure how to get it into that form algebraically or even what the hints are that I should do that...?

Thanks