Proof Inverse Sin: Complete Series Proof

[bfd]

Can someone tell me where I can find a complete proof of the infinite series used to find the arcsin? thanks in advance.

 

[nicksauce]

http://planetmath.org/encyclopedia/TaylorSeriesOfArcusSine.html

 

[bfd]

http://planetmath.org/encyclopedia/TaylorSeriesOfArcusSine.html

Thank you for link. I apologize I should have been more specific with my question.

I actually wanted to see a proof or some method that specifically creates arcsin. I ask because I was tutoring a student one day in trig and was trying to get the angle of sin based on the output of the sin with that unknown angle. To make a long story short I realized I never needed the angle measure to begin with but I was curious to see if there's a way to get the angle of a trig function just based on using the unit circle. I guess that's my real question: is there a way to get arcsin just by using the unit circle?