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Documentation/Calc Functions/TANH

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Function name:

TANH

Category:

Mathematical

Summary:

Calculates the hyperbolic tangent (tanh) of a hyperbolic angle expressed in radians.

Syntax:

TANH(Number)

Returns:

Returns a real number in the range (-1, 1) that is the hyperbolic tangent 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 tangent is to be calculated.

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

Additional details:

The formula for the hyperbolic tangent of x is:

[math]\displaystyle{ \tanh(x)~=~\frac{\sinh(x)}{\cosh(x)}~=~\frac{e^x-e^{-x}}{e^x+e^{-x}} }[/math]

The figure below illustrates the function TANH.

TANH function

Examples:

Formula Description Returns
=TANH(0) Hyperbolic tangent of 0. 0
=TANH(D1) where cell D1 contains the number -2. Hyperbolic tangent of -2. −0.964027580075817
=ATANH(TANH(3)) The hyperbolic tangent of 3 radians is taken and then the inverse hyperbolic tangent of that value is calculated. 3

Related LibreOffice functions:

ATANH

COSH

COTH

CSCH

FISHERINV

SECH

SINH

ODF standard:

Section 6.16.70, part 2

Related (or similar) Excel functions:

TANH