Consider the following. x = sin 1/2 θ , y = cos 1/2 θ , −π ≤ θ ≤ π Eliminate the parameter to find a Cartesian equation of the curve

Question

I am confused on how to separate the variables and make the cartesian equation. Thanks for any help.

Answer 1

x² +y²=sin² (1/2 θ) + cos² (1/2 θ)=1

x² +y²=1

Since −π ≤ θ ≤ π, it will be the upper semicircle

y= √(1-x²), -1≤x≤1