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.

Hyperbolic Functions The two basic hyperbolic functions are "sinh" and "cosh": Hyperbolic Sine: sinh (x) = ex − e-x 2 (pronounced "shine") Hyperbolic Cosine: cosh (x) = ex + e-x 2 (pronounced "cosh") They use the natural exponential function ex And are not the same as sin (x) and cos (x), but a little bit similar: sinh vs sin cosh vs cos Catenary

The Hyperbolic Cosine Function. cosh (x) = (e x + e −x) / 2 Don't confuse it with the cosine function cos (x):

Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch Definition of hyperbolic functions Hyperbolic sine of x \displaystyle \text {sinh}\ x = \frac {e^ {x} - e^ {-x}} {2} sinh x = 2ex −e−x …

2015年12月25日 · 【功能简介】求变量的双曲余弦和反双曲余弦。 【语法格式】 1．Y=cosh (X) 计算X中元素的双曲余弦值，元素x的双曲余弦等于 (ex+e-x)/2。 2．Y=acosh (X) 计算X中元素的反双曲余弦，元素x的反双曲余弦等于log [x+ (x2-1)1/2]。 【实例5.4】求元素的双曲余弦和反双曲余 …

In applied mathematics, hyperbolic functions are equivalents to regular trigonometric functions but expressed by means of the hyperbola instead of a circle. While the points (cos t, sin t) are …

Definition 4.11.1 The hyperbolic cosine is the function coshx = ex + e − x 2, and the hyperbolic sine is the function sinhx = ex − e − x 2. . Notice that cosh is even (that is, cosh(− x) = cosh(x)) while sinh is odd (sinh(− x) = − sinh(x)), and coshx + sinhx = ex.

So for some suitable t t, cosh t cosh t and sinh t sinh t are the coordinates of a typical point on the hyperbola. In fact, it turns out that t t is twice the area shown in the first graph of Figure 4.11.2 4.11.

Cosh is defined as the ratio of the adjacent side of a right triangle to the hypotenuse, where the hypotenuse is the distance between the origin and a point on the hyperbola. This ratio is always greater than or equal to one, and it increases as the angle between the adjacent side and the hypotenuse increases.

2024年11月6日 · 本文将详细介绍cosh函数的计算方法及其在实际中的应用。 首先，我们需要了解cosh函数的定义。 cosh (x)定义为 (e^x + e^ (-x))/2，其中e是自然对数的底数，约等于2.71828。 从这个定义可以看出，cosh函数是一个偶函数，即cosh (-x) = cosh (x)。