# How to use the ACOSH function

**What is the ACOSH function?**

The ACOSH function calculates the inverse hyperbolic cosine of a number.

**What is the cosine of a number?**

The cosine ratio is the adjacent side divided by the hypotenuse of a right triangle.

cosine Î¸ = adjacent side / hypotenuse

**What is the hyperbolic cosine of a number?**

The hyperbolic cosine is a hyperbolic function defined as:

cosh(x) = (e^x + e^-x)/2

**What are hyperbolic functions?**

Hyperbolic functions are similar to ordinary trigonometric functions, but they use a different shape to define them.

Trigonometric functions use a circle, while hyperbolic functions use a hyperbola. The chart above shows a hyperbola and two asymptotes (dashed lines) where the intersection is at the center of the hyperbola.

The unit hyperbola looks like this:

It shows x^{2} -y^{2}=1 and x^{2} -y^{2}=-1

**What is the inverse hyperbolic cosine of a number?**

arccosh(x) = ln(x + âˆš(x^{2} - 1))

The inverse hyperbolic cosine finds the hyperbolic whose hyperbolic cosine equals the input. It is the inverse of the hyperbolic cosine function, similar to how arccos is the inverse of regular cosine.

**What is the angle Î¸?**

The Greek letter theta (Î¸) is commonly used to represent an unknown angle in a right triangle. The ACOS function returns the angle Î¸ expressed in radians.

**What is a right triangle?**

A right triangle is a type of triangle that contains one internal angle measuring 90 degrees or Ï€/2 radians (a right angle).

**What are radians?**

Radians are a unit used to measure angles. An angle of 1 radian has an arc length equal to the circle's radius.

**What is the relationship between the number pi and radians?**

Radians measure angles by the length of the arc they make in a circle rather than degrees. The full circumference of any circle is 2Ï€ multiplied by the circle's radius (2Ï€r).

Since the circumference goes all the way around a circle, that means the full circle measures 2Ï€ radians. Half a circle would be Ï€ radians (half of 2Ï€). A quarter circle is 2Ï€/4 = Ï€/2 radians. An eighth of a circle is 2Ï€/8 = Ï€/4 radians.

Excel has a function that returns the number pi:Â PI function

**What is an hyperbolic arc?**

A hyperbolic arc is a segment of a hyperbola analogous to a circular arc on a circle. It is a curved segment cut out from a hyperbola by two intersecting asymptotes. Defined by two hyperbola points and the curve between them. Its length can be calculated using hyperbolic trigonometric functions.

**What is a hyperbolic's radius?**

The radius of a hyperbola is not a well-defined term, because a hyperbola does not have the shape of a circle.

**What are degrees?**

Degrees are a unit used to measure angles. It is based on dividing a full circle into 360 equal parts. Degrees are divided into fractional parts like minutes and seconds for more precision.

**What is the relationship between radians and degrees?**

The circumference of a circle is 360 degrees or 2Ï€ radians.

360 degrees = 2Ï€ radians

which is

degrees = radians x (180 / Ï€)

Excel has two functions for converting between radians and degrees:Â RADIANSÂ |Â DEGREES

Formula in cell C3:

### Excel Function Syntax

ACOSH(*number*)

### Arguments

number |
Required. Any real number equal to or greater than 1. |

### Comments

ACOSH(COSH(*number*)) equalsÂ *number.*

## How to plot a hyperbolic triangle?

### Functions in 'Math and trigonometry' category

The ACOSH function function is one of 73 functions in the 'Math and trigonometry' category.

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