I'm having issues with the following problem.
Let $a$ be a positive real number. A spacecurve $K_{a}$ in the $(x,z)$-plane is given by
$$s(u)=(a\sin(u)\cos(u),0,\cos(u)),\ \ u\in[0,\frac{\pi}{2}]$$.
Determine the parametrization of the surface $F$ in the $(x,z)$-plane that is bounded by $K_{\frac{1}{2}}$ and $K_{1}$.
I've struggled with this parametrization for quite a bit now and I can't seem to get it working... My attempt was the following
$$r(u,v)=(0.5\sin(u)\cos(u),0,v\sin(u)\cos(u)),\ \ u\in[0,\frac{\pi}{2}],v\in[0,1]$$
Any help is highly appreciated!