well when you take the inverse of any function, the domain and range switch. For trigonometric functions, however, the inverse would not be a function because it would not pass the "vertical line test", therefore you have to restrict the domain.

for example:
sin(x)
D: pi/2 to -pi/2
R: 1 to -1
arcsin(x) [another way of saying sin^-1(x)]
D: 1 to -1
R: pi/2 to -pi/2

now say you want to find the arcsin(1/2)
looking at the unit circle, we know that the sine function is = to (1/2) at the angle pi/6 (radians)
so the arcsin(1/2) = pi/6 (radians)

so the arcsin(3/5) = 4/5

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