COTH
Returns the hyperbolic cotangent of an angle. COTH(x) = 1/TANH(x).
COTH(number)Arguments
numberAny nonzero real number.
=COTH(2)Hyperbolic cotangent of 2
=COTH(0.5)Hyperbolic cotangent of 0.5
- •Available since Excel 2013
- •Returns #DIV/0! if number is 0
- •COTH(x) = (eˣ + e⁻ˣ) / (eˣ - e⁻ˣ)
- •Passing 0 to COTH, which returns a #DIV/0! error since hyperbolic cotangent is undefined at zero (it's the reciprocal of hyperbolic tangent, which is 0 at that point)
- •Confusing COTH with COT - COTH is the hyperbolic cotangent, unrelated to angles or the unit circle, while COT is the regular trigonometric cotangent based on an angle in radians
- •Expecting the result to stay within a bounded range like -1 to 1 - unlike TANH, COTH's output grows unbounded as the input approaches zero from either side
TANHCalculates the hyperbolic tangent, the reciprocal relationship to what COTH calculates (COTH(x) = 1/TANH(x)).SINHCalculates the hyperbolic sine, one of the two building blocks (along with hyperbolic cosine) that define COTH.COTCalculates the regular (non-hyperbolic) cotangent of an angle, a different function despite the similar name.Why does COTH return a #DIV/0! error?
The input is 0 - hyperbolic cotangent is undefined at that point, since it's the reciprocal of hyperbolic tangent, which equals 0 when the input is 0.
Is COTH related to angles the way COT is?
No, COTH takes a plain real number, not an angle - it has no connection to radians, degrees, or the unit circle, unlike its trigonometric namesake COT.
Does COTH's result stay between -1 and 1 like TANH's does?
No, that's the opposite pattern - TANH is bounded between -1 and 1, but COTH (its reciprocal) grows toward infinity as the input approaches 0, and only approaches ±1 for large inputs.
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