One high brow remark
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I think this would be a really good opportunity to really explain to them why taking the positive square root is correct. As written the solution is fine but this is a good spot to make this question a learning moment (as opposed to some "oh I just memorized the derivative of arcsin moment") and to get students to think "Oh yea why can I ignore the negative branch?"
Just my two cents - do you agree?
Something like "Since the domain of arcsin is [-\pi/2, \pi/2], we see that cos is a positive function on this interval and hence we can take the positive branch".
Again is this necessary no but I think it would be nice to include because to a student I think this is non-obvious.