hyperbolic sine
Hyperbolic sine
The sh function allows to calculate online the hyperbolic sine of a number.
Hyperbolic sine 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 sine function is written sh, it is defined by the following formula :
`sh(x)=(exp(x)-exp(-x))/2`
exp is the notation of the exponential function.
- Calculation of the hyperbolic sine
- Derivative of hyperbolic sine
- Antiderivative of hyperbolic sine
- Limits of hyperbolic sine
- The hyperbolic sine function has a limit in `-oo` which is `-oo`.
- The hyperbolic sine function has a limit in `+oo` which is `+oo`.
The hyperbolic sine calculator allows through the sh function to calculate online the hyperbolic sine of a number.
To calculate the hyperbolic sine of a number, just enter the number and apply the sh function. For calculating the hyperbolic sine of the next number 0, enter sh(`0`) or directly 0, if the button sh appears already, the result 0 is returned.
The derivative of the hyperbolic sine is equal to ch(x).
The antiderivative of the hyperbolic sine is equal to ch(x).
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The limits of the hyperbolic sine exist at `-oo` and `+oo`:
- `lim_(x->-oo)sh(x)=-oo`
- `lim_(x->+oo)sh(x)=+oo`
Syntax :
sh(x), x is a number.
Other notation sometimes used : sinh
Examples :
sh(`2`), returns 3.62686040785
Derivative hyperbolic sine :
To differentiate function hyperbolic sine online, it is possible to use the derivative calculator which allows the calculation of the derivative of the hyperbolic sine function
The derivative of sh(x) is derivative(`"sh"(x)`)=`"ch"(x)`
Antiderivative hyperbolic sine :
Antiderivative calculator allows to calculate an antiderivative of hyperbolic sine function.
An antiderivative of sh(x) is antiderivative(`"sh"(x)`)=`"ch"(x)`
Limit hyperbolic sine :
The limit calculator allows the calculation of limits of the hyperbolic sine function.
The limit of sh(x) is limit(`"sh"(x)`)
Graphic hyperbolic sine :
The graphing calculator is able to plot hyperbolic sine function in its definition interval.
Property of the function hyperbolic sine :
The hyperbolic sine function is an odd function.- 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.