The function ch calculates online the hyperbolic cosine of a number.

Hyperbolic cosine 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 cosine function is written ch, it is defined by the following formula :

`ch(x)=(exp(x)+exp(-x))/2`

exp is the notation of the exponential function.

Calculation of the hyperbolic cosine

The hyperbolic cosine calculator allows through the ch function to calculate online the hyperbolic cosine of a number.

To calculate the hyperbolic cosine of a number, just enter the number and apply the ch function. For calculating the hyperbolic cosine of the next number 0, enter ch(`0`) or directly 0, if the button ch appears already, the result 1 is returned.

Derivative of hyperbolic cosine

The derivative of the hyperbolic cosine is equal to sh(x).

Antiderivative of hyperbolic cosine

The antiderivative of the hyperbolic cosine is equal to sh(x).

Limits of hyperbolic cosine

The limits of the hyperbolic cosine exist at `-oo` and `+oo`:
• The hyperbolic cosine function has a limit in `-oo` which is 0.
`lim_(x->-oo)ch(x)=0`
• The hyperbolic cosine function has a limit in `+oo` which is `+oo`.
`lim_(x->+oo)ch(x)=+oo`

Syntax :

ch(number)

Other notation sometimes used : cosh

Examples :

ch(`2`) returns `3.76219569108`

Derivative hyperbolic cosine :

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

The derivative of ch(x) is derivative(`"ch"(x)`)=`"sh"(x)`

Antiderivative hyperbolic cosine :

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

An antiderivative of ch(x) is antiderivative(`"ch"(x)`)=`"sh"(x)`

Limit hyperbolic cosine :

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

The limit of ch(x) is limit(`"ch"(x)`)

Graphic hyperbolic cosine :

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

Property of the function hyperbolic cosine :