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.

在 数学 中， 双曲函数 是一类与常见的 三角函数 （也叫圆函数）类似的函数。 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数，其自变量的值叫做 双曲角。 双曲函数出现于某些重要的线性 微分方程 的解中，譬如說定义 悬链线 和 拉普拉斯方程。 最簡單的幾種雙曲函數為 [1]： {\displaystyle \tanh x= {\frac {\sinh x} {\cosh x}}= {\frac {e^ {x} …

$\text{cosh} (x + 2k \pi i) = \text{cosh}\ x$ $\text{sech} (x + 2k\pi i) = \text{sech} x$ $\text{tanh} (x + k\pi i) = \text{tanh}\ x$ $\text{coth} (x + k\pi i) =\text{coth} x$ Relationship between inverse hyperbolic and inverse trigonometric functions

sech(x) = 1 cosh(x) = 2 e x + e-x . Hyperbolic cosecant "csch" or "cosech": csch(x) = 1 sinh(x) = 2 e x − e-x. Why the Word "Hyperbolic" ? Because it comes from measurements made on a Hyperbola: So, just like the trigonometric functions relate to a circle, the hyperbolic functions relate to a hyperbola. Identities. sinh(−x) = −sinh(x ...

Hyperbolic Definitions sinh(x) = ( e x - e-x)/2 . csch(x) = 1/sinh(x) = 2/( e x - e-x) . cosh(x) = ( e x + e-x)/2 . sech(x) = 1/cosh(x) = 2/( e x + e-x) . tanh(x ...

This is an online free sech calculator. You can calculate value of sech () trignometric function easily using this tool. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides.

There are main six hyperbolic functions, namely sinh x, cosh x, tanh x, coth x, sech x, csch x. What are Hyperbolic Trig Identities? The hyperbolic trig identities are formulas of hyperbolic functions which are analogous to trigonometric functions. Some of the hyperbolic trig identities are: sinh(x ± y) = sinh x cosh y ± coshx sinh y

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 …

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.

2023年7月28日 · The hyperbolic secant (sech) is the reciprocal of the hyperbolic cosine: sech(x) = 1 / cosh(x), and the hyperbolic cosecant (csch) is the reciprocal of the hyperbolic sine: csch(x) = 1 / sinh(x). These formulas not only define the hyperbolic functions but also illustrate their close connection to exponential functions.