## Purpose

## Return value

## Syntax

`=SINH(number)`

*number*- The hyperbolic angle.

## How to use

The SINH function returns the hyperbolic sine of a number. Given the input 1, the function returns the value 1.175201194.

`=SINH(0) // returns 1.175201194`

### Explanation

The hyperbolic sine function returns the vertical component of the point on the right branch (x ≥ 1) of the unit hyperbola corresponding to the hyperbolic angle given as input.

Together with hyperbolic cosine, the functions parameterize the right branch of the unit hyperbola given by the equation x² - y² = 1. In plain language, this means that the two functions trace out the shape of the right branch of the unit hyperbola.

Given a hyperbolic angle corresponding to a point on the hyperbola's curve, SINH returns the *vertical component* of the point, while COSH returns the horizontal component of the point. For example, given the hyperbolic angle -1, hyperbolic cosine returns the x-component 1.543080635, and hyperbolic sine returns the y-component -1.175201194.

Here is a table that shows some points on the unit hyperbola formed by COSH and SINH.

As the hyperbolic angle increases positively, the vertical component goes to infinity, and as the hyperbolic angle increases negatively, the vertical component goes to negative infinity. This is different from the sine function, which is periodic and repeats values.

*Images courtesy of wumbo.net.*