Documentation/Calc Functions/COTH
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Function name:
COTH
Category:
Mathematical
Summary:
Calculates the hyperbolic cotangent (coth) of a hyperbolic angle expressed in radians.
Syntax:
COTH(Number)
Returns:
Returns a real number that lies outside the range [-1, 1] that is the hyperbolic cotangent of the specified hyperbolic angle.
Arguments:
Number is a non-zero real number, or a reference to a cell containing that number, that is the hyperbolic angle in radians whose hyperbolic cotangent is to be calculated.
- If Number is non-numeric, then COTH reports a #VALUE! error.
- If Number is equal to 0, then COTH reports a #NUM! error.
Additional details:
The formula for the hyperbolic cotangent of x is:
[math]\displaystyle{ \coth(x)~=~\frac{\cosh(x)}{\sinh(x)}~=~\frac{e^x+e^{-x}}{e^x-e^{-x}} }[/math]
The figure below illustrates the function COTH.
Examples:
Formula | Description | Returns |
---|---|---|
=COTH(1) | Hyperbolic cotangent of 1. | 1.31303528549933 |
=COTH(D1) where cell D1 contains the number -2. | Hyperbolic cotangent of -2. | −1.03731472072755 |
=ACOTH(COTH(3)) | The hyperbolic cotangent of 3 radians is taken and then the inverse hyperbolic cotangent of that value is calculated. | 3 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
COTH since v.2013.