The arcsine function, denoted as arcsin(x) or sin^(-1)(x), is the inverse of the sine function, used to determine an angle whose sine value is a given number. It is defined for values in the interval [-1, 1] and returns angles in the range [-π/2, π/2] radians or [-90°, 90°] degrees, making it essential in trigonometry for solving problems involving right-angled triangles and periodic phenomena.