Can I find this trigonometric expression without a calculator?

Question

I know that $\sin A= 0.75$ will give me the answer of $A= 48.6^\circ$ or $\ 131^\circ$. Is there a way to find what $A$ equals manually. Thank you.

Answer 1

The Macluarin series for arcsin$(A)$ can be found here: http://scipp.ucsc.edu/~haber/ph116A/taylor11.pdf and it converges pretty quickly, so you can just use the first several terms and get a good approximation when you plug in $A = 0.75$.