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

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 …

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 …

There are six hyperbolic functions are sinh x, cosh x, tanh x, coth x, sech x, csch x. In this article, we will define these hyperbolic functions and their properties, graphs, identities, derivatives, …

coth 2 (x) - csch 2 (x) = 1. arcsinh (z) = ln ( z + (z 2 + 1) ) arccosh (z) = ln ( z (z 2 - 1) ) arctanh (z) = 1/2 ln ( (1+z)/ (1-z) ) arccsch (z) = ln ( (1+ (1+z 2) )/z ) arcsech (z) = ln ( (1 (1-z 2) )/z ) …

Jul 28, 2023 · Hyperbolic Cotangent (coth). Coth(x) is the reciprocal of tanh(x), i.e., coth(x) = 1 / tanh(x) . It finds applications in various engineering and physics problems.

Feb 6, 2021 · The coth function involves two functions, $\cosh{x}$ divided by $\sinh{x}$. This animation illustrates this: When $x$ is large and negative, $\sinh{x}$ becomes ever closer to $ …

Illustrated definition of Coth: The Hyperbolic Cotangent Function. coth(x) (esupxsup esupminusxsup) (esupxsup minus...

To calculate, enter the angle at which the hyperbolic cotangent should be calculated, then click on the 'Calculate' button. The unit of measurement for the angle can be switched between …

\( \coth^{-1} A = \dfrac{1}{2}\ln \left(\dfrac{x+1}{x-1} \right) \; , \; |x| \gt 1\) Derivative of Hyperbolic Functions and Their Inverses