Yes, arcsine is the inverse of sine. It's the reflection of sine across the line y = x
arcsin(sin(theta)) = theta
Since sin(theta) is periodic, the inverse is not technically a function (it doesn't pass the single input -> single output test). The output of arcsin is always single valued by cropping it off between -pi/2 and pi/2 radians. This is most easily understood by looking at a graph of arcsin.
sin(arcsin(n)) = n, where -1 <= n <= 1
The limits make sense when you realize that sin(theta) is always a value between -1 and 1.
pi is the ratio of the circumference of a circle to the diameter of said circle.
It's hidden in the angle in this problem.
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