Hyperbolic cosine : How to use it?
The function ch calculates online the hyperbolic cosine of a number.
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 :
The hyperbolic cosine function is an even function.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.
- The hyperbolic cosine function has a limit in `+oo` which is `+oo`.
- `lim_(x->-oo)ch(x)=0`
- `lim_(x->+oo)ch(x)=+oo`
- 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 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.
- Trigonometric Calculator : simplify_trig. Calculator wich uses trigonometric formula to simplify trigonometric expression.
- Cosine : cos. The cos trigonometric function calculates the cos of an angle in radians, degrees or gradians.
- Cosecant : cosec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
- Cotangent : cotan. The cotan trigonometric function to calculate the cotan 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.
- Secant : sec. The trigonometric function sec allows to calculate the secant of an angle expressed in radians, degrees, or grades.
- Sine : sin. The sin trigonometric function to calculate the sin of an angle in radians, degrees or gradians.
- Tangent : tan. The tan trigonometric function to calculate the tan of an angle in radians, degrees or gradians.