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 =) 

Basically you can use infinite series to calculate approximation of inverse trigonometric functions.
$$
\arcsin z = z+ \left( \frac 12 \right) {z^3 \over 3} + \left( {1 \cdot 3 \over 2 \cdot 4} \right){z^5 \over 5} + \left( {1 \cdot 3 \cdot 5 \over 2 \cdot 4 \cdot 6} \right){z^7 \over 7}\ +\ ... \; = \sum_{n=0}^\infty {\binom{2n}{n}z^{2n+1} \over 4^n(2n+1)}; \;\;\; |z| \le 1
$$
$$
    \arccos z = \frac \pi2 - \arcsin z = \frac \pi2 - \sum_{n=0}^\infty {\binom{2n}{n}z^{2n+1} \over 4^n(2n+1)}; \;\;\; |z| \le 1
$$
$$
    \arctan z = z-{z^3 \over 3}+{z^5 \over 5}-{z^7 \over 7}\ +\ ... \ =  \sum_{n=0}^\infty{(-1)^nz^{2n+1} \over 2n+1}; \;\;\;|z|\le1, \; z\neq i, -i
$$
