# Hyperbolic sinus

If you have to calculate the hyperbolic sine of a number real x, our online calculator provides you with the result of that calculation immediately.

Just enter the number x into the calculator and press the calculate button to obtain the hyperbolic sine. If you wish, we also have at your disposal another tool for calculating the hyperbolic cosine.

## Hyperbolic sine formula

The hyperbolic sine of a real number x is computed by solving the formula above of these lines.

As you can see, it is important to be familiar with the equations exponentials.

## Properties of the hyperbolic sine

The hyperbolic function sinh (x) has a series of properties you should know to be able to solve the exercises properly. Some of these properties are the following:

• Its domain ranges from (-∞, +∞).
• It is a bijective, increasing, transcendent and odd function.

In addition, it has these relations that will be very useful to you for the exercises:

• sinh (x+y) = sinh coshy + coshx sinhy
• senh (x-y) = senh coshy - coshx senhy
• sinh2x = 2senhx coshx
• sinh2 (x) = cosh2(x) - 1

## Hyperbolic sine of 0

Now that we know more about the hyperbolic function sinh (x), let's solve some typical exercises. In this case, we are going to calculate how much is sinh(0):

sinh(0) = (e0 - e-0) / 2 = (1 - 1) / 2  = 0

Therefore, we can verify that the hyperbolic sine of 0 equals zero.

## Hyperbolic sine of 1

Now let's see what result we get by calculating sinh(1):

sinh(1) = (eπ - e) / 2 = (2,718 - 0,368) / 2 = 1,175

## Hyperbolic sine of pi

Let's finish with these solved exercises of the hyperbolic sine calculating its value for π (pi):

sinh(π) = (e1 - e-1) / 2 = (23,139 - 0,043) / 2 = 11,548

If you have any problems withesolving the hyperbolic sine If you have any questions please leave us a comment and we will try to help you as soon as possible.

## Derivative of the hyperbolic sine

The derivative of senh (u) is equal to the hyperbolic cosine of that function multiplied by the derivative of its function. If instead of a function we have senh (x), where x is a real number, the derivative will be:

d/dx sinh(x) = cosh(x)

## Integral of sinh (x)

In the same way, here we have the integral of senh (u).

## Calculate hyperbolic sine in Excel

If you have the Excel spreadsheet program installed on your computer or mobile device, then you can also solve the hyperbolic cosine of a number using Microsoft software.

Just open a new spreadsheet and type in an empty cell the following formula:

=SENOH()

Between the parentheses you must write the number for which you want to calculate the senh (x) or a cell in which that quantity is written. Either method is valid.

## Inverse hyperbolic sine

Finally, we leave you with the formula for the inverse hyperbolic sine as in some cases we may also be asked to do so.