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.

Article sections

## 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 r**elations that will be very useful to you** for the exercises:

- sinh (x+y) = sinh coshy + coshx sinhy
- sinh (x-y) = sinh coshy - coshx sinhy
- sinh2x = 2senhx coshx
- sinh
^{2}(x) = cosh^{2}(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) = (e

^{0}- 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) = (e

^{π}- e^{-π}) / 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) = (e

^{1}- e^{-1}) / 2 = (23,139 – 0,043) / 2 = 11,548

If you have any problems with**esolving 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.