I have a function to calculate sinus from this library. How can I calculate arcus sinus and arcus cosine?
The library you are referring to approximates sin and cos via piecewise linear function. This approach is applicable to arcsin and arccos functions as well, you just need different table of points.
Also, as long as you already have sin function, you may find
y = arcsin(x) by solving
sin y = x equation using bisection method, or some other method for finding equation roots.