Summary :

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

Description :

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 :

• Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccos function is the inverse functions of the cosine function.
• Arcsine : arcsin. The arcsin function allows the calculation of the arc sine of a number. The arcsin function is the inverse function of the sine function.
• Arctangent : arctan. The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
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• Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.