arctangent

Calculus arctan

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Function : arctan

Summary :

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

arctan online

Description :

Arctangent function

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

  1. Calculation of the arctangent
  2. 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.

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

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

  7. Limits of arctangent
  8. 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`

The arctan function allows the calculation of the arctangent of a number. The arctangent 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_calculator(`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_calculator(`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_calculator(`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.
Calculate online with arctan (arctangent)
See also :
  • Arccosine : arccos. The arccos function allows the calculation of the arc cosine of a number. The arccosine 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 arcsine function is the inverse function of the sine function.
  • Arctangent : arctan. The arctan function allows the calculation of the arctangent of a number. The arctangent function is the inverse functions of the tangent function.
  • Cosine : cos. The cos trigonometric function calculates the cosine of an angle in radians, degrees or gradians.
  • Cotangent : cotan. The cotan trigonometric function to calculate the cotangent of an angle in radians, degrees or gradians.
  • Trigonometric expansion : expand_trigo. The calculator makes it possible to obtain the trigonometric expansion of an expression.
  • Trigonometric linearization : linearization_trigo. Calculator that allows to linearize a trigonometric expression.
  • Simplify Calculator : simplify. Calculator wich can simplify an algebraic expression online.
  • Sine : sin. The sin trigonometric function to calculate the sine of an angle in radians, degrees or gradians.
  • Tangent : tan. The tan trigonometric function to calculate the tangent of an angle in radians, degrees or gradians.
  • Trigonometric Calculator : trig_calculator. Calculator wich uses trigonometric formula to simplify trigonometric expression.