Also, similarly to how the derivatives of sin(t) and cos(t) are cos(t) and –sin(t) respectively, the derivatives of sinh(t) and cosh(t) are cosh(t) and sinh(t) respectively. Hyperbolic functions are used to express the angle of parallelism in hyperbolic geometry .

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

$\text{cosh}\ x\ \text{cosh}\ y = \frac12(\text{cosh}(x + y) + \text{cosh} (x - y))$ $\text{sinh}\ x\ \text{cosh}\ y = \frac12(\text{sinh}(x + y) + \text{sinh} (x - y))$ Expression of hyperbolic functions in terms of others

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

2024年11月25日 · In trigonometry, the coordinates on a unit circle are represented as (cos θ, sin θ), whereas in hyperbolic functions, the pair (cosh θ, sinh θ) represents points on the right half of an equilateral hyperbola.

Y = cosh(X) returns the hyperbolic cosine of the elements of X. The cosh function operates element-wise on arrays. The function accepts both real and complex inputs.

The hyperbolic cosine function, or cosh(x), is one of the various hyperbolic functions. Its evaluation involves Euler’s number e . For an input x , the hyperbolic cosine’s output is the sum of e to the power x and e to the power minus x, divided by 2.

If $(x,y)$ is a point on the right half of the hyperbola, and if we let $x=\cosh t$, then $\ds y=\pm\sqrt{x^2-1}=\pm\sqrt{\cosh^2 t-1}=\pm\sinh t$. So for some suitable $t$, $\cosh t$ and $\sinh t$ are the coordinates of a typical point on the hyperbola.

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.

The two basic hyperbolic functions are sinh and cosh. sinh(x) = (e x − e −x)/2 cosh(x) = (e x + e −x)/2 (From those two we also get the tanh, coth, sech and csch functions.) Here you see how sinh compares to the sine function and cosh compares to the cosine function: