The arcsine function, denoted as arcsin(x) or sin^(-1)(x), is the inverse function of the sine function within the domain [-1,1]. It returns the angle in radians between -π/2 and π/2 whose sine is the given number x.

The formula for arcsine is:

arcsin(x) = sin^(-1)(x) = y, where -π/2 ≤ y ≤ π/2 and sin(y) = x

For example, the arcsine of 0.5 is π/6 radians (or 30 degrees), since sin(π/6) = 0.5.