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.

The two basic hyperbolic functions are "sinh" and "cosh": Hyperbolic Sine: sinh(x) = e x − e-x 2 (pronounced "shine") Hyperbolic Cosine: cosh(x) = e x + e-x 2 (pronounced "cosh") They use the natural exponential function e x. And are not the same as sin(x) and cos(x), but a little bit similar: sinh vs sin. cosh vs cos. Catenary

Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch Definition of hyperbolic functions. Hyperbolic sine of x $\text{sinh}\ x = \frac{e^{x} - e^{-x}}{2}$ Hyperbolic cosine of x $\text{cosh}\ x = \frac{e^x + e^{-x}}{2}$ Hyperbolic tangent of x $\text{tanh}\ x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$ Hyperbolic cotangent of x

Illustrated definition of Cosh: The Hyperbolic Cosine Function. cosh (x) (esupxsup esupminusxsup) 2 Dont confuse it with...

2024年11月25日 · Learn the different hyperbolic trigonometric functions, including sine, cosine, and tangent, with their formulas, examples, and diagrams. Also, learn their identities.

2025年1月31日 · This function describes the shape of a hanging cable, known as the catenary. It is implemented in the Wolfram Language as Cosh[z]. Special values include cosh0 = 1 (2) cosh(lnphi) = 1/2sqrt(5), (3) where phi is the golden ratio.

Definition 4.11.1 The hyperbolic cosine is the function $$\cosh x ={e^x +e^{-x }\over2},$$ and the hyperbolic sine is the function $$\sinh x ={e^x -e^{-x}\over 2}.$$ $\square$

Cosh, short for hyperbolic cosine, is a mathematical function that is part of the family of hyperbolic functions. It is closely related to the hyperbolic sine function and is used extensively in the study of calculus, particularly in the context of the calculus of hyperbolic functions.