Suppose we want to parametrize the boundary curve of hemisphere $x^2+y^2+z^2=16, y\ge0$, oriented in the direrction of the positive $y-$axis. The answer the book gives is $r(t)=<4\cos(-t),0, 4\sin(-t)>$, and this confuses me because "direrction of the positive $y-$axis" means positive(counter-clockwise) orientation of the circle on $xz$ plane. Why is there negative $t$?
2026-03-28 05:22:55.1774675375
What's the direction of parametrization for the following question?
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Because in the $xz$ plane, $ z= r\cos\theta$ and $x= r\sin \theta $.