## csch x

### The term “csch x” refers to the hyperbolic cosecant function, which is a mathematical function defined for any real value of x

The term “csch x” refers to the hyperbolic cosecant function, which is a mathematical function defined for any real value of x.

The hyperbolic cosecant function is defined as the reciprocal of the hyperbolic sine function (sinh x). The definition of csch x is given as:

csch x = 1 / sinh x

In terms of exponential functions, csch x can also be written as:

csch x = (2 / (e^x – e^(-x)))

Since the hyperbolic sine function sinh x has an infinite range, the hyperbolic cosecant function csch x will have a range of all real numbers except 0. It approaches positive or negative infinity as x approaches 0.

The graph of csch x resembles the shape of a reciprocal function, with vertical asymptotes at x = 0. As x approaches positive or negative infinity, csch x approaches 0.

It is worth mentioning that the hyperbolic cosecant function (csch x) is not commonly used in everyday mathematics, but it has applications in various branches of science and engineering, specifically in the fields of physics and electrical engineering.

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