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...

Omni's cosh calculator will help you quickly compute the values of the hyperbolic cosine function as well as discover its most important properties. In the short article below, we discuss the following topics: What cosh x is and why is it called hyperbolic? Can you meet cosh in real life? (Spoiler: yes) What does the plot of cosh look like?

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.

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.

Mar 5, 2025 · This definition implies that cosh is an even function, meaning cosh(-x) = cosh(x). Additionally, the derivative of cosh(x) is sinh(x), and the integral of cosh(x) is sinh(x). The hyperbolic cosine function also satisfies several identities, including cosh^2(x) - sinh^2(x) = 1, which is analogous to the Pythagorean identity for sine and cosine.

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.

The cosh function has several important properties that are useful in a variety of mathematical contexts. Some of the most important properties of the cosh function include: Continuity: The cosh function is continuous for all real values of x. Differentiability: The cosh function is differentiable for all real values of x.