COTH
Calculate the hyperbolic cotangent of a number in Excel with COTH.
Math & Trigonometry
| Excel 2013+
| Google Sheets Supported
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Syntax
=COTH(number)
Returns: Number Arguments
| Argument | Required | Description |
|---|---|---|
| number | Yes | The angle in radians for which you want to calculate the hyperbolic cotangent. |
About
COTH returns the hyperbolic cotangent of a hyperbolic angle. Use this function when working with hyperbolic trigonometry in engineering or physics calculations where you need to model exponential growth and decay, such as heat transfer, electrical circuits, or wave mechanics.
This function works with radians and is the hyperbolic version of the regular COT function. While regular trigonometry uses circles, hyperbolic functions use hyperbolas, which makes them useful for modeling real-world phenomena like catenary curves (the shape of a hanging cable) or relativistic calculations. For related hyperbolic calculations, check out TANH and COSH.
COTH is available in Excel 2013 and later versions, including Microsoft 365.
This function works with radians and is the hyperbolic version of the regular COT function. While regular trigonometry uses circles, hyperbolic functions use hyperbolas, which makes them useful for modeling real-world phenomena like catenary curves (the shape of a hanging cable) or relativistic calculations. For related hyperbolic calculations, check out TANH and COSH.
COTH is available in Excel 2013 and later versions, including Microsoft 365.
Examples
Values approaching zero
Watch how COTH produces increasingly large values as inputs approach zero. Try changing the values to numbers even closer to zero to see the dramatic growth.
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Converting degrees to radians
COTH expects radians, not degrees. See the difference when you use degrees directly versus converting them first with RADIANS.
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Error protection with IFERROR
Use IFERROR to handle problematic inputs gracefully. Try entering different values to see how error protection helps maintain clean results.
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Watch out for
⚠
Number too large
Using values where the absolute value is 2^27 or greater returns a #NUM! error.
→ Keep your input values below 134,217,728. Most practical applications use much smaller values anyway.
⚠
Non-numeric input
Providing text or blank cells returns a #VALUE! error.
→ Verify your input is numeric. Use ISNUMBER() to check values before passing them to COTH, or wrap the formula in IFERROR() to handle errors gracefully.
⚠
Using degrees instead of radians
COTH expects radians, not degrees, which produces incorrect results if you pass degree measurements.
→ Convert degrees to radians first using the RADIANS function: =COTH(RADIANS(A2)).
Tips & notes
The input value must have an absolute value less than 2^27 (approximately 134 million). COTH is mathematically defined as COSH(number)/SINH(number), which equals (e^number + e^-number)/(e^number - e^-number).
Common questions
What's the difference between COT and COTH?
COT calculates the circular cotangent used in standard trigonometry with triangles and circles. COTH calculates the hyperbolic cotangent, which models exponential relationships and appears in physics and engineering problems involving hyperbolas.
When would I actually use COTH in Excel?
COTH appears in specialized engineering calculations like transmission line theory, heat transfer equations, and certain physics models. Most general Excel users won't need it, but it's important for technical fields that work with hyperbolic functions.
Can I use COTH with very small numbers?
Yes, but be careful near zero. COTH approaches infinity as the input approaches zero from either direction, which can cause calculation issues. For values very close to zero, you might get extremely large results or errors.