Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. They also occur in the solutions of many linear differential equations (such as the equation …

The hyperbolic function occurs in the solutions of linear differential equations, calculation of distance and angles in the hyperbolic geometry, Laplace’s equations in the cartesian …

The two basic hyperbolic functions are "sinh" and "cosh": sinh (x) = ex − e-x 2. cosh (x) = ex + e-x 2. They use the natural exponential function ex. And are not the same as sin (x) and cos (x), …

我们所熟知的三角函数也被叫做circular function，因为sin、cos满足 \sin^2 x+\cos^2 x=1 可以看出是从一个单位圆的方程 x^2+y^2=1 中演化过来的。 而圆锥曲线我们知道还有 双曲线 、抛物线 …

最基本的双曲函数是 雙曲正弦 函数 和 雙曲餘弦 函数 ，从它们可以导出 双曲正切 函数 等，其推导也类似于三角函数的推导。 双曲函数的反函数称为 反双曲函数。 双曲函数的定义域是实 …

Roughly speaking ordinary trigonometric functions are trigonometric functions of purely real num-bers, and hyperbolic functions are trigonometric functions of purely imaginary numbers.

Hyperbolic functions are expressed in terms of the exponential function e x. There are six hyperbolic functions are sinh x, cosh x, tanh x, coth x, sech x, csch x. In this article, we will …

In this unit we define the three main hyperbolic functions, and sketch their graphs. We also discuss some identities relating these functions, and mention their inverse functions and …

Formulas for the Inverse Hyperbolic Functions From the graphs of the hyperbolic functions, we see that all of them are one-to-one except cosh’ and sech’. If we restrict the domains of these …

2023年8月29日 · All six hyperbolic functions can now be defined in general, analogous to the trigonometric (circular) functions: The graphs of the hyperbolic functions are shown below: