Arctangent : How to use it?
The arctan function allows the calculation of the arctan of a number. The arctan function is the inverse functions of the tangent function.
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 :
The arctangent function is an odd 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`.
- The arctangent function has a limit in `+oo` which is `-pi/2`.
- `lim_(x->-oo)arctan(x)=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` |
- 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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