# Documentation/Calc Functions/COSH

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COSH

Mathematical

## Summary:

Calculates the hyperbolic cosine (cosh) of a hyperbolic angle expressed in radians.

COSH(Number)

## Returns:

Returns a real number in the range [1, ∞) that is the hyperbolic cosine of the specified hyperbolic angle.

## Arguments:

Number is a real number, or a reference to a cell containing that number, that is the hyperbolic angle in radians whose hyperbolic cosine is to be calculated.

• If Number is non-numeric, then COSH reports a #VALUE! error.

The formula for the hyperbolic cosine of x is:

$\displaystyle{ \cosh(x)~=~\frac{e^x+e^{-x}}{2} }$

The figure below illustrates the function COSH.

COSH function

## Examples:

Formula Description Returns
=COSH(0) Hyperbolic cosine of 0. 1
=COSH(D1) where cell D1 contains the number -2. Hyperbolic cosine of -2. 3.76219569108363
=ACOSH(COSH(3)) The hyperbolic cosine of 3 radians is taken and then the inverse hyperbolic cosine of that value is calculated. Note that =ACOSH(COSH(-3)) also returns 3, because COSH is an even function. 3

COSH