integration – inverse trigonometric functions

I currently have integrals classes at my university and I have problems when I need to define inverse trigonometric functions at certain intervals.
My main problem is how to know without (arcsin (x)), arcssin (without (x)), cos (arccos (x)), … and so on. Is there any logical way to think that leads me to the solution or, at least, to a table where you can see all its values ​​in full intervals? [0,2π].
I researched this topic online and only found solutions for intervals [-π/2,π/2] and I know that this is something that I should be familiar with, but I tend to mix them shortly after remembering how each one goes.