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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