SOLUTION: can someone give me some guidance on how to rewrite as an algebraic expression sin(arctan(x))=sin theta?

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Question 1003933: can someone give me some guidance on how to rewrite as an algebraic expression
sin(arctan(x))=sin theta?
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let alpha = arctan(x).

Then tan%28alpha%29 = x = sin%28alpha%29%2Fcos%28alpha%29             ----->

x%5E2 = sin%5E2%28alpha%29%2Fcos%5E2%28alpha%29 = sin%5E2%28alpha%29%2F%281+-+sin%5E2%28alpha%29%29     ----->

x%5E2%2A%281+-+sin%5E2%28alpha%29%29 = sin%5E2%28alpha%29         ----->

x%5E2 - x%5E2.sin%5E2%28alpha%29 = sin%5E2%28alpha%29       ----->

x%5E2 = %281%2Bx%5E2%29.sin%5E2%28alpha%29                 ----->

sin%5E2%28alpha%29 = %28x%5E2%29%2F%281+%2B+x%5E2%29,

sin%28alpha%29 = sqrt%28%28x%5E2%29%2F%281%2Bx%5E2%29%29 = +/- %28abs%28x%29%29%2F%28sqrt%281%2Bx%5E2%29%29 = x%2F%28sqrt%281%2Bx%5E2%29%29.

Finally,   sin(arctan(x)) = x%2F%28sqrt%281%2Bx%5E2%29%29.

Is this what you want?