How to use the COTH function
What is the COTH function?
The COTH function calculates the hyperbolic cotangent of a hyperbolic angle. The function has been available since Excel 2013.
What is the hyperbolic cotangent of a hyperbolic angle?
The hyperbolic cotangent is a hyperbolic function defined as:
coth x = (e^x + e^-x)/(e^x - e^-x)
The COTH(number) function returns the same value as
- 1/TANH(number)
- COSH(number)/SINH(number)
What is e?
The number e is an irrational constant that is approximately equal to 2.71828. It is the base of the natural logarithm function, which is denoted by ln. The natural logarithm function is the inverse of the natural exponential function, which is denoted by ex. This means that if y = ex, then x = ln y.
What is a hyperbole?
Hyperbolic functions are similar to ordinary trigonometric functions, but they use a different shape to define them called hyperbolas.
The chart above shows a hyperbola and two asymptotes (dashed lines) where the intersection is at the center of the hyperbola.
The unit hyperbola looks like this:
It shows x2Â -y2=1 and x2Â -y2=-1
These functions get closer, however, they never crosses or touches these dashed lines (asymptotes).
What are the hyperbolic cosine asymptotes?
The asymptotes of the hyperbolic cosine function are the lines:
- y = +∞
- y = -∞,
This means that the function never crosses or touches these lines, but gets closer and closer to them as x goes to +infinity or -infinity.
What are the main hyperbolic functions, their domain and range?
| Hyperbolic | Domain | Range |
| sinh(x) | All real numbers | (-∞, ∞) |
| cosh(x) | All real numbers | [1, ∞) |
| tanh(x) | All real numbers | (-1, 1) |
| sech(x) | All real numbers | (0, 1) |
What is the hyperbolic domain?
The domain of a hyperbolic function refers to the set of input values it is defined and valid for.
What is the hyperbolic range?
The range of a hyperbolic function refers to the set of possible output values it returns.
| Hyperbolic Function | Formula | Asymptotes |
| sinh | sinh x = (e^x - e^-x)/2 | y = e^x/2 and y = -e^-x/2 |
| cosh | cosh x = (e^x + e^-x)/2 | y = 0 and y = ∞ |
| tanh | tanh x = (e^x - e^-x)/(e^x + e^-x) | y = -1 and y = 1 |
| coth | coth x = (e^x + e^-x)/(e^x - e^-x) | x = nπ and y = -1 and y = 1 |
| sech | sech x = 2/(e^x + e^-x) | y = 0 and y = ∞ |
| csch | csch x = 2/(e^x - e^-x) | x = nπ and y = 0 and y = ∞ |
1. COTH function Syntax
COTH(number)
2. COTH function Arguments
| number | Required. A numerical value. |
3. COTH function example
4. COTH function notworking
The COTH function returns
- #VALUE! error value if number is a nonnumeric value.
- #NUM! error value if number is outside the valid range which is 2^27.
Formula in cell C3:
Functions in 'Math and trigonometry' category
The COTH function function is one of many functions in the 'Math and trigonometry' category.
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