Interactive Mathematics by Kunio Mitsuma, Ph.D.

KU Interactive Mathematics

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Inverse Sine Function

Function	Domain	Range
y = sin(x)	–π/2 ≤ x ≤ π/2	–1 ≤ y ≤ 1
y = arcsin(x)	–1 ≤ x ≤ 1	–π/2 ≤ y ≤ π/2

The restriction on the domain of the original function is necessary so that it satisfies the Horizontal Line Test. Observe that the domain and range flip over between the two functions.
The graphs are symmetrical with respect to the line y = x.