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.

cosh (z) = cos (iz) sech (z) = sec (iz) tanh (z) = -i tan (iz) coth (z) = i cot (iz)

Hyperbolic Trig Identities is like trigonometric identities yet may contrast to it in specific terms. The fundamental hyperbolic functions are hyperbola sin and hyperbola cosine from which the other trigonometric functions are inferred. You can easily explore …

$\text{cosh}(x \pm y) = \text{cosh}\ x\ \text{cosh}\ y \pm \text{sinh}\ x\ \text{sinh}\ y$ $\text{tanh}(x \pm y) = \frac{\text{tanh}\ x \pm \text{tanh}\ y}{1 \pm \text{tanh}\ x \cdot \text{tanh}\ y}$ $\text{coth}(x \pm y) = \frac{\text{coth x}\ \text{coth}\ y \pm l}{\text{coth}\ y \pm \text{coth}\ x}$

(\cosh x + \sinh x)^{n} = \cosh (nx) + \sinh (nx) \qquad (n \in \mathbb{N}) \\ \color{blue}{\textbf{反双曲函数的定义}} \sinh ^{-1} x=\ln (x+\sqrt{x^{2}+1}) \quad(-\infty,+\infty) \\ \cosh ^{-1} x=\ln …

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.

2023年7月28日 · One of the fundamental hyperbolic trig identities is the hyperbolic Pythagorean identity: cosh^2(x) - sinh^2(x) = 1. This identity bears resemblance to the Pythagorean identity in circular trigonometry, but here we deal with hyperbolic functions. Another useful identity is the hyperbolic addition formula for the hyperbolic tangent: tanh(x + y ...

2024年11月24日 · cosh算法，即双曲余弦函数算法，是数学和计算机科学中常用的函数之一。 它广泛应用于工程计算、物理建模、图像处理等领域。 本文将深入探讨cosh算法的原理，并介绍其在实际应用中的案例。

What is the value of cosh (pi) ?

Important Identity of cosh. Cosh, along with sinh, have various identities that look analogous to identities for the regular trigonometric functions of cos and sin, with a slight change in the signs. The identity looks like this: \[\cosh^{2} x-\sinh^{2} x = 1\]