The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.

Arcsine function

The arcsine function is the inverse function of the sine function, it allows to calculates the arc sine of a number online.

The number on which you wish to apply the arcsine function must belong to the range [-1,1].

Calculation of the arcsine

To calculate the arcsine of a number, just enter the number and apply the arcsin function. Thus, for calculating the arcsine of the number following 0.4, you must enter arcsin(`0.4`) or directly 0.4, if the arcsin button already appears, the result 0.411516846067 is returned.

Derivative of arcsine

The derivative of the arcsine is equal to `1/sqrt(1-(x)^2)`.

Antiderivative of arcsine

The antiderivative of the arcsine is equal to `x*arcsin(x)+sqrt(1-(x)^2)`.

Table of remarkable values

arcsin(`-1`)	`-pi/2`
arcsin(`-sqrt(3)/2`)	`-pi/3`
arcsin(`-sqrt(2)/2`)	`-pi/4`
arcsin(`-1/2`)	`-pi/6`
arcsin(`0`)	`0`
arcsin(`1/2`)	`pi/6`
arcsin(`sqrt(2)/2`)	`pi/4`
arcsin(`sqrt(3)/2`)	`pi/3`
arcsin(`1`)	`pi/2`

Syntax :

arcsin(x) where x is a number.

Other notation sometimes used : asin

Examples :

arcsin(`0`) returns 0

Derivative arcsine :

To differentiate function arcsine online, it is possible to use the derivative calculator which allows the calculation of the derivative of the arcsine function

The derivative of arcsin(x) is derivative(`"arcsin"(x)`)=`1/sqrt(1-(x)^2)`

Antiderivative arcsine :

Antiderivative calculator allows to calculate an antiderivative of arcsine function.

An antiderivative of arcsin(x) is antiderivative(`"arcsin"(x)`)=`x*"arcsin"(x)+sqrt(1-(x)^2)`

Limit arcsine :

The limit calculator allows the calculation of limits of the arcsine function.

The limit of arcsin(x) is limit(`"arcsin"(x)`)

Inverse function arcsine :

The inverse function of arcsine is the sine function noted sin.

Graphic arcsine :

The graphing calculator is able to plot arcsine function in its definition interval.

Property of the function arcsine :