How to derive the branch cuts for complex arcsin(z)

[monmon_4]

I notice that the branch cuts for arcsin(z) are from -infinity to -1 and 1 to infinity. How do these choices for the branch cuts make the function single-valued? I am having trouble understanding the reasoning here even though these choices for the cuts are widely used/accepted.

 

[FactChecker]

I believe that any two paths from -1 and 1 to infinity that don't intersect themselves or each other (i.e. leaves the complex plane connected) will work. The standard ones seem like a good choice. They are simple and symmetric wrt the real axis.