Hyperbolic cosecant function

The ratio of number $2$ to subtraction of the negative natural exponential function from the positive natural exponential function is called the hyperbolic cosecant function.

Introduction

$e$ is a positive irrational mathematical constant and take $x$ as a variable. The positive and negative natural exponential functions are written in mathematics as $e^x$ and $e^{-x}$ respectively.

The subtraction of the negative natural exponential function from positive natural exponential function is $e^x-e^{-x}$

The ratio of the quantity $2$ to the subtraction of them is written mathematically as follows.

$\large \dfrac{2}{e^x-e^{-x}}$

In mathematics, the ratio of $2$ to the subtraction of the natural exponential functions is called the hyperbolic co-secant function. It is denoted by either ${\mathop{\rm cosech}\nolimits}$ or ${\mathop{\rm csch}\nolimits}$ but the function is expressed in terms of $x$. Therefore, the hyperbolic cosecant function is written as ${\mathop{\rm cosech}\nolimits}{x}$ or ${\mathop{\rm csch}\nolimits}{x}$ mathematically.

$\large {\mathop{\rm csch}\nolimits}{x} \,=\, \dfrac{2}{e^x-e^{-x}}$

Latest Math Topics
Apr 18, 2022
Apr 14, 2022

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved