# Documentation/Calc Functions/ASINH

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ASINH

Mathematical

## Summary:

Calculates the inverse hyperbolic sine (arsinh) of a real number, in radians.

ASINH(Number)

## Returns:

Returns a real number that is the inverse hyperbolic sine of Number in radians.

## Arguments:

Number is a real number, or a reference to a cell containing that number, whose inverse hyperbolic sine is to be calculated.

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

The formula for the inverse hyperbolic sine of x is:

$\displaystyle{ \operatorname{arsinh}(x) = \ln\left (x+\sqrt{(x^2+1)}\right ) }$

The figure below illustrates the function ASINH.

ASINH function

## Examples:

Formula Description Returns
=ASINH(-90) Inverse hyperbolic sine of -90. -5.19298771365894
=ASINH(SINH(4)) Inverse hyperbolic sine of hyperbolic sine of 4. 4
=ASINH(D1) where cell D1 contains the number 0.5. Inverse hyperbolic sine of 0.5. 0.481211825059603

ASINH