what is The COSH function ?

[beingchinmay]

The COSH trigonometric function returns the hyperbolic cosine of the specified number. The specification for the COSH function is:


FUNCTION COSH (n NUMBER) RETURN NUMBER;

If n is a real number and i = −1 (the imaginary square root of −1), then the relationship between COS and COSH can be expressed as follows:

COS (i * n) = COSH (h)

[damponting44]

COSH function:
In the C Programming Language, the cosh function returns the hyperbolic cosine of x.
Syntax:
double cosh(double x);

[richardmsmith]

It is nothing but The mathematical hyperbolic cosine function.
Return the hyperbolic cosine of different numbers:
Example:
SELECT COSH(0)
Output:1.00

[brookeroberts7]

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric functions defined for the hyperbola rather than on the circle: just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola.

[Lishmalinyjames]

We may also use hyperbolic functions to define distance in specific non-Euclidean geometry, which means estimating the angles and distances in hyperbolic geometry.

[saravanan28]

The COSH trigonometric function returns the hyperbolic cosine of the specified number. The function is defined as:

FUNCTION COSH (n NUMBER) RETURN NUMBER;

If n is a real number and i =  −1 (the imaginary square root of −1), then the relationship between COS and COSH can be expressed as follows:

COS (i * n) = COSH (n)


The hyperbolic cosine (COSH) function is a mathematical function that gives the value of the hyperbolic cosine of a given input number. It is often used in mathematics, physics, and engineering to model various natural phenomena.

The relationship between the trigonometric cosine (COS) and the hyperbolic cosine (COSH) can be expressed as:

COS (i * n) = COSH (n)

This relationship demonstrates the connection between the trigonometric functions and the hyperbolic functions when dealing with complex numbers.


The hyperbolic cosine function is defined as the sum of the exponential function and its inverse:

COSH(n) = (e^n + e^(-n)) / 2

This function is used to model various phenomena in mathematics, physics, and engineering, especially when dealing with exponential growth or decay. The relationship COS(i * n) = COSH(n) shows how the trigonometric cosine function can be connected to the hyperbolic cosine function when complex numbers are involved. This relationship allows for the extension of trigonometric functions into the realm of complex numbers and provides a useful connection between real and complex analysis.