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(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.
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.