Question

Use spherical coordinates to find a parametrization of the quarter-sphere x2+y2+z2=a2, z ≥ 0, x ≥ 0

Answer 1

alright, let's represent this in spherical coordinates

Answer 2

\[\rho=a\]

Answer 3

\[\theta=-90 \text{ to } 90\]

Answer 4

\[\phi=0 to 90\]

Answer 5

and you follow the miracle

Answer 6

\[x=\rho sin(\phi)cos(\theta)\]
\[y=\rho sin(\phi) sin(\theta)\]
\[z=\rho cos(\theta)\]