Number.Cosh
NumberReturns the hyperbolic cosine of a number.
Syntax
Number.Cosh(number as nullable number) as nullable numberParameters
| Name | Type | Required | Description |
|---|---|---|---|
number | number | Yes | The number whose hyperbolic cosine is computed. |
Return Value
number — The hyperbolic cosine of the number, always >= 1.
Remarks
Number.Cosh returns the hyperbolic cosine, defined mathematically as:
cosh(x) = (e^x + e^(−x)) / 2
Unlike the circular cosine, which oscillates between -1 and 1, the hyperbolic cosine grows without bound. Its minimum value is 1, occurring at x = 0. It is an even function: cosh(−x) = cosh(x), meaning it is symmetric about the y-axis. For large positive or negative x, cosh grows roughly as e^|x| / 2.
Hyperbolic functions do not operate in degrees or radians — they take a real number argument directly and produce a real result. This contrasts with circular trigonometric functions like Number.Cos.
The fundamental identity cosh²(x) − sinh²(x) = 1 is the hyperbolic analog of the Pythagorean identity. In data transformation, hyperbolic functions appear in physics models (catenary shape of cables), certain statistical distributions (e.g., the logistic function uses tanh), and financial risk models. Most Power Query users will not encounter them in everyday work.
Examples
Example 3: Verify the hyperbolic identity cosh²(x) − sinh²(x) = 1
let
X = 3,
Identity = Number.Cosh(X)^2 - Number.Sinh(X)^2
in
Number.Round(Identity, 10)The final output — Number.Round applied to 10 decimal places, confirming the hyperbolic identity result rounds to exactly 1.
Result | |
|---|---|
| 1 | 1 |