The arccos function allows the calculation of the arc cosine of a number. The arccos function is the inverse functions of the cosine function.

Arccosine function

The arccosine function is the inverse function of the cosine function, it calculates the arc cosine of a number online.

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

Calculation of the arccosine

To calculate the arccosine of a number, just enter the number and apply the arccos function. Thus, for calculating the arccosine of the number following 0.4, you must enter arccos(`0.4`) or directly 0.4, if the arccos button already appears, result 1.15927948073 is returned.

Derivative of arccosine

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

Antiderivative of arccosine

The antiderivative of the arccosine is equal to `x*arccos(x)-sqrt(1-(x)^2)`.

Table of remarkable values

arccos(`-1`)	`pi`
arccos(`-sqrt(3)/2`)	`5*pi/6`
arccos(`-sqrt(2)/2`)	`3*pi/4`
arccos(`-1/2`)	`2*pi/3`
arccos(`0`)	`pi/2`
arccos(`1/2`)	`pi/3`
arccos(`sqrt(2)/2`)	`pi/4`
arccos(`sqrt(3)/2`)	`pi/6`
arccos(`1`)	`0`

Syntax :

arccos(x) where x is a number.

Other notation sometimes used : acos

Examples :

arccos(`1`) returns 0

Derivative arccosine :

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

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

Antiderivative arccosine :

Antiderivative calculator allows to calculate an antiderivative of arccosine function.

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

Limit arccosine :

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

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

Inverse function arccosine :

The inverse function of arccosine is the cosine function noted cos.

Graphic arccosine :

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