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

$e$ is a positive irrational mathematical constant and assume, $x$ is a variable. So, the positive natural exponential function is denoted by $e^x$ and the negative natural exponential function is represented by $e^{-x}$.

The subtraction of negative natural exponential function from positive natural exponential function is written as $e^x\,–\,e^{-x}$.

The ratio of subtraction of them to number $2$ is written as the below mathematical form.

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

The ratio of them is called the hyperbolic sine function. The hyperbolic sine is simply written as $\sinh$ in short form but the function is expressed in terms of $x$. Therefore, the hyperbolic sine function is written as $\sinh{x}$ in mathematics.

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

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Oct 22, 2024

Oct 17, 2024

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved