Relationship between arctan2, arcsin, and arccos

Question

I believe the reason for using atan2 in most computational settings is due to the fact that it returns an unambiguous value for a given input. How does atan2 relate to the other inverse trig functions, namely asin and acos? How can I convert between the operations?

Answer 1

atan2(y,x) is supposed to be the angle of the complex number $\arg\{x + iy\}$ and is supposed to be correct for all quadrants. setting $$\arg\{x+iy\} = \arctan\left(\tfrac{y}{x}\right)$$ is correct only if $x>0$.

about the other relationships of the inverse trig functions, these are in books and tables of trig and inverse trig identities.