I’m not sure I understand what you were trying to do here. From what I understand, sin/cos/tan are just a way of getting the ratios between the angles… Not sure what that means exactly though. I know that if I take the arcsin of something I can get the degrees of one of the angles, but not sure which angle LOL. Could you elaborate?
Lets take sin for example. Sin of an angle is the side opposed to that angle (facing) divided by the hypothensus.
asin (O/H) is thus the angle of our triangle.
This is particularly important for polar coordinates where we need that angle to locate our vector. Polar coordinates are particularly important in complex and quaternions fields.