Question

find parametrization of the surface...

Answer 1

spherical band. the portion of the sphere x^2 + y^2 + z^2 = 3 between the planes z = sqrt(3) / 2 and z = - sqrt (3) / 2

Answer 2

find the angle first

Answer 3

I think that the requested parametrization is given by the subsequent formulas:
\[\Large \left\{ \begin{gathered}
x = \sqrt 3 \sin u\cos v \hfill \\
y = \sqrt 3 \sin u\sin v \hfill \\
z = \sqrt 3 \cos u \hfill \\
\end{gathered} \right.,\quad \begin{array}{*{20}{c}}
{\frac{\pi }{3} \leqslant u \leqslant \frac{{2\pi }}{3}} \\
{0 \leqslant v \leqslant 2\pi }
\end{array}\]

Answer 4

since we have this situation:

so theta runs from pi/3 to 2*pi/3