Arc Sine
The arc sine of a number x is a real number for which the sine is [latex]x[/latex].
The argument [latex]x[/latex] of the arc sine relationship is a real number between [latex]-1[/latex] and [latex]+1[/latex].
The relation defined by [latex]y [/latex]= arcsin([latex]x[/latex]) is not a function.
Notation
The symbol used for the arc sine of a number [latex]x[/latex] is “arcsin([latex]x[/latex])” which is generally read as “arc sine of [latex]x[/latex].”Examples
In the sexagesimal system of measuring angles, we have:- arcsin(0,5) = 30
- arcsin(0,5) = 180n ± 30 where n is an integer.
Educational Note
The arc sine function is the reciprocal of the sine function defined in the interval [latex]\left[ -\dfrac {\pi } {2},\dfrac {\pi } {2}\right][/latex] which is the function [latex]f[/latex] of the interval [latex]\left[ -\dfrac {\pi } {2},\dfrac {\pi } {2}\right][/latex] on the interval [latex]\left[ -1,1\right][/latex] so that [latex]f\left( x\right)[/latex] is the only real number for which the sine is x.
Some authors use the notation [latex]\sin ^{-1}x[/latex] to indicate the arc sine of [latex]x[/latex], but this notation is already used to refer to the inverse of a number and can therefore create confusion with the inverse of a sine function called the cosecant function.