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Homework Statement
So using standard spherical polar co-ordinates, my notes define a sphere as
r(s,t) = aCos(s)Sin(t) i + aSin(s)Sin(t) j + aCos(t) k
and the normal to the surface is given by the cross product of the two partial differentials:
[itex]\partial[/itex]r[itex]/\partial[/itex]s X [itex]\partial[/itex]r[itex]/dt[/itex]
So my issue is what is in my notes where:
[itex]\partial[/itex]r[itex]/\partial s[/itex]= -aSin(s)Sin(t) i + aCos(s)Sin(t) j + aCot(t) k
It is the final part that I don't understand. Why is the partial differential of Cos(t) with respect to s Cot(t)? I would have calculated it as zero.
Homework Equations
[itex]\partial[/itex][itex]/[/itex][itex]\partial[/itex]s (aCos(t)) = aCot(t) ?
The Attempt at a Solution
All I can think is that it's using a trig identity? As I understand it the k component should only depend upon t, not just from the above equations but in spherical polar co-ordinates in general, at least how I'm picturing it.
Thanks in advance for any help.