How do you actually calculate inverse $\sin, \cos, $ etc. ? I started to wonder, how does one actually calculate the $\arcsin, \arccos, $ etc. without a calculator? For example I know that: 
$$\arccos(0.3) = 72.54239688^{\circ}$$
by an online calculator, but how would one calculate this with a pencil and paper? How is it done? :) I can't remember any math teacher talk about this? How is it actually implemented? 
Thnx for any help =) 

You don't, because you actually can't (except a few specific values). And that applies to most real functions, actually...
You can, however, calculate some good approximation, for example with appropriate polynomials.
