In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than 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 unit hyperbola.

From sinh and cosh we can create: tanh (x) = sinh (x) cosh (x) = ex − e-x ex + e-x. coth (x) = cosh (x) sinh (x) = ex + e-x ex − e-x. sech (x) = 1 cosh (x) = 2 ex + e-x. csch (x) = 1 sinh (x) = 2 ex − e-x. Why the Word "Hyperbolic" ? Because it comes from measurements made on a Hyperbola:

Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…

In this short lesson, you will learn about Tanh hyperbolic function and its properties including tanh function, tanh calculator, tanh formula, and tanh equation. You can see the graphical representation of the Tanh function in the image below.

$\text{tanh} (x + k\pi i) = \text{tanh}\ x$ $\text{coth} (x + k\pi i) =\text{coth} x$ Relationship between inverse hyperbolic and inverse trigonometric functions

The hyperbolic tangent function is an old mathematical function. It was first used in the work by L'Abbe Sauri (1774). This function is easily defined as the ratio between the hyperbolic sine and the cosine functions (or expanded, as the ratio of the half‐difference and half‐sum of two exponential functions in the points and ):

This tanh calculator is the ultimate tool you need to deal with the hyperbolic tangent function! In what follows, we will explain what tanh is in math and how to calculate both the inverse and the derivative of tanh .

TANH (x) returns the hyperbolic tangent of the angle x. The argument x must be expressed in radians. To convert degrees to radians you use the RADIANS function.

Sep 10, 2020 · The tanh function involves two functions, $\sinh{x}$ divided by $\cosh{x}$. This animation illustrates this: When $x$ is zero, $\sinh x$ is 0 and $\cosh x$ is 1, so the result is 0.

The tanh() function returns the hyperbolic tangent of a number. The hyperbolic tangent is equivalent to sinh(number) / cosh(number). The tanh() function is defined in the <math.h> header file.