The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.

Arctangent function

The arctan function is the inverse function of the tangent function, it calculates the arc tangent of a number online.

Calculation of the arctangent

To calculate the arctangent of a number, just enter the number and apply the arctan function.

For example, to calculate the arctangent of the following number 10, type arctan(`10`), or directly 10 if the arctan button already appears, the result 1.4711276743 is returned.

Derivative of arctangent

The derivative of the arctangent is equal to `1/(1+(x)^2)`.

Antiderivative of arctangent

The antiderivative of the arctangent is equal to `x*arctan(x)-1/2*ln(1+(x)^2)`.

Limits of arctangent

The limits of the arctangent exist at `-oo` (minus infinity) and `+oo` (plus infinity):
• The arctangent function has a limit in `-oo` which is `pi/2`.
`lim_(x->-oo)arctan(x)=pi/2`
• The arctangent function has a limit in `+oo` which is `-pi/2`.
`lim_(x->+oo)arctan(x)=-pi/2`

Table of remarkable values

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

Syntax :

arctan(x) , x is a number.

Other notation sometimes used : atan

Examples :

arctan(`0`) returns 0

Derivative arctangent :

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

The derivative of arctan(x) is derivative(`"arctan"(x)`)=`1/(1+(x)^2)`

Antiderivative arctangent :

Antiderivative calculator allows to calculate an antiderivative of arctangent function.

An antiderivative of arctan(x) is antiderivative(`"arctan"(x)`)=`x*"arctan"(x)-1/2*ln(1+(x)^2)`

Limit arctangent :

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

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

Inverse function arctangent :

The inverse function of arctangent is the tangent function noted tan.

Graphic arctangent :

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

Property of the function arctangent :

• 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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• Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
• Cotangent : cotan. The cotan trigonometric function to calculate the cotan of an angle in radians, degrees or gradians.
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• Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.