hyperbolic cotangent

Calculus coth

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Function : coth

Summary :

The coth function calculates online the hyperbolic cotangent of a number.

Coth online

Description :

Hyperbolic cotangent function

The calculator allows you to use most hyperbolic functions, it is possible to calculate the hyperbolic cosine (noted ch or cosh), the hyperbolic sine (noted sh or sinh ), the hyperbolic tangent (noted th or tanh ), and the hyperbolic cotangent (noted coth or cotanh ).

The hyperbolic cotangent function is written coth, it is defined by the following formula :

`coth(x)=1/(th(x))=(ch(x))/(sh(x))`

  1. Calculation of the hyperbolic cotangent
  2. The hyperbolic cotangent calculator allows through the coth function to calculate online the hyperbolic cotangent of a number.

    To calculate the hyperbolic cotangent of a number, enter the number and to apply the coth function. For calculating the hyperbolic cotangent of the following number 2, enter coth(2) or directly 2, if the coth button already appears, the result 1.03731472073 is returned.

  3. Derivative of hyperbolic cotangent
  4. The derivative of the hyperbolic cotangent is equal to `-1/(sh(x))^2`.

  5. Antiderivative of hyperbolic cotangent
  6. The antiderivative of the hyperbolic cotangent is equal to `ln(|sh(x|)`.

  7. Limits of hyperbolic cotangent
    • The limits of the hyperbolic cotangent exist at `-oo` (minus infinity) and `+oo` (plus infinity):
    • The hyperbolic cotangent function has a limit in `-oo` which is `-1`.
      • `lim_(x->-oo)coth(x)=-1`
    • The hyperbolic cotangent function has a limit in `+oo` which is `1`.
      • `lim_(x->+oo)coth(x)=1`

The coth function calculates online the hyperbolic cotangent of a number.


Syntax :

coth(x), where x is a number.

Other notation sometimes used : cotanh


Examples :

coth(2), returns 1.03731472073


Derivative hyperbolic cotangent :

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

The derivative of coth(x) is derivative(coth(x))=`-1/(sh(x))^2`


Antiderivative hyperbolic cotangent :

Antiderivative calculator allows to calculate an antiderivative of hyperbolic cotangent function.

An antiderivative of coth(x) is antiderivative(coth(x))=`ln(sh(x))`


Limit hyperbolic cotangent :

The limit calculator allows the calculation of limits of the hyperbolic cotangent function.

The limit of coth(x) is limit(coth(x))


Graphic hyperbolic cotangent :

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



Property of the function hyperbolic cotangent :

The hyperbolic cotangent function is an odd function.
Calculate online with coth (hyperbolic cotangent)
See also :
  • Exponential : exp. The function exp calculates online the exponential of a number.
  • Hyperbolic cosine : ch. The function ch calculates online the hyperbolic cosine of a number
  • Hyperbolic cotangent : coth. The coth function calculates online the hyperbolic cotangent of a number.
  • Hyperbolic sine : sh. The sh function allows to calculate online the hyperbolic sine of a number.
  • Hyperbolic tangent : th. The function th allows to calculate online the hyperbolic tangent of a number.
  • 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.