The Excel COTH function returns the hyperbolic cotangent of a number — the reciprocal of the hyperbolic tangent, 1/TANH. The argument is a plain number, not an angle.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | Any non-zero real number. COTH is the reciprocal of TANH, so an argument of 0 returns a #DIV/0! error. |
How to use it
COTH is simply 1/TANH(number), introduced in Excel 2013. There is no degree-vs-radian issue — you pass a plain number:
COTH is an odd function whose magnitude is always greater than 1, approaching 1 as the input grows. Use =1/TANH(x) in versions before Excel 2013.
Undefined at zero. Because TANH(0) is zero, =COTH(0) returns a #DIV/0! error. Use any non-zero argument.
Try it: interactive demo
Pick a COTH example to see the formula and its result.
Practice workbook
Frequently asked questions
What is the hyperbolic cotangent?
COTH(x) = 1/TANH(x). It is an odd function, undefined at x = 0, and its magnitude is always greater than 1.Which Excel versions have COTH?
=1/TANH(x) instead.Why does COTH(0) return an error?
=COTH(0) returns #DIV/0!. Use any non-zero argument.Does COTH use degrees or radians?
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