ACOTH
Returns the inverse hyperbolic cotangent of a number. The absolute value of the number must be greater than 1.
ACOTH(number)Arguments
numberA real number with |number| > 1.
=ACOTH(6)Inverse hyperbolic cotangent of 6
=ACOTH(-2)Inverse hyperbolic cotangent of -2
- •Available since Excel 2013
- •Returns #NUM! if -1 ≤ number ≤ 1
- •ACOTH(x) = 0.5 × LN((x+1)/(x-1))
- •Passing a number between -1 and 1 (inclusive), which returns a #NUM! error since the inverse hyperbolic cotangent is only defined for inputs with an absolute value strictly greater than 1
- •Confusing ACOTH with ACOT - ACOTH deals with hyperbolic cotangent values outside the range -1 to 1, while ACOT is the regular (non-hyperbolic) arccotangent, defined for every real number
- •Assuming the result is an angle - like other inverse hyperbolic functions, ACOTH's output is a dimensionless value with no direct radians-to-degrees conversion the way regular trigonometric inverses have
COTHPerforms the inverse operation conceptually - calculates the hyperbolic cotangent, though Excel doesn't provide a direct COTH function, requiring 1/TANH(x) instead.ATANHCalculates the inverse hyperbolic tangent, a closely related function through the identity ACOTH(x) = ATANH(1/x).ACOTCalculates the regular (non-hyperbolic) arccotangent, a different function despite the similar name, valid across all real numbers.Why does ACOTH return a #NUM! error?
The absolute value of the input is 1 or less - the inverse hyperbolic cotangent is only mathematically defined for numbers strictly greater than 1 or strictly less than -1.
How is ACOTH related to ATANH?
They're connected through the identity ACOTH(x) = ATANH(1/x) - since Excel has ATANH but no separate hyperbolic cotangent function, this relationship is sometimes useful for cross-checking results.
Does ACOTH work with negative numbers?
Yes, as long as the number is less than -1 - ACOTH(-2) is a valid calculation and returns a negative result.
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