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.

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

\color{blue}{\textbf{双曲函数的定义}} 1、双曲正弦 \sinh x = \frac{e^{x} - e^{-x}}{2} \\ 2、双曲余弦 \cosh x = \frac{e^{x} + e^{-x}}{2} \\ 3、双曲正切 \sinh x =\frac{\sinh}{\cosh} = \frac{e^{x} - e^{…

cosh (x) = ( e x + e -x )/2. sech (x) = 1/cosh (x) = 2/ ( e x + e -x ) tanh (x) = sinh (x)/cosh (x) = ( e x - e -x )/ ( e x + e -x ) coth (x) = 1/tanh (x) = ( e x + e -x)/ ( e x - e -x ) cosh 2 (x) - sinh 2 (x) = 1. tanh 2 (x) + sech 2 (x) = 1. coth 2 (x) - csch 2 (x) = 1. arcsinh (z) = ln ( …

Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch Definition of hyperbolic functions. Hyperbolic sine of x $\text{sinh}\ x = \frac{e^{x} - e^{-x}}{2}$ Hyperbolic cosine of x $\text{cosh}\ x = \frac{e^x + e^{-x}}{2}$ Hyperbolic tangent of x $\text{tanh}\ x = \frac{e^x - e^{-x}}{e^x + e^{-x}}$ Hyperbolic cotangent of x

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.

在 數學 中， 雙曲餘弦 是一種 雙曲函數，是 雙曲幾何 中，與歐幾里得幾何的 餘弦函數 相對應的函數。 雙曲餘弦一般以cosh表示 [1]，在部分較舊的文獻中有時會以 表示。 [2] 雙曲餘弦可以用來描述 悬链线，即兩端固定自然下垂的繩索，因此可以用於進行 悬索桥 的工程計算。 雙曲餘弦一般記為 [3] （有時會簡寫為 [4]），其在 複分析 中定義為： 其中 是 複變指數函數 （日语：複素指数函数）。 由于已知的技术原因，图表暂时不可用。 带来不便，我们深表歉意。 綠色線為雙曲 …

公式1 \sinh x=\frac {e^x-e^ {-x}} {2},\cosh x=\frac {e^x+e^ {-x}} {2},\tanh x=\frac {e^x-e^ {-x}} {e^x+e^ {-x}}\\ \mathrm {csch}x=\frac {1} {\sinh x},\mathrm {sech}x=\frac {1} {\cosh x},\mathrm {coth}x=\frac {1} {\tanh x}\\ 公式2 \cosh z=\cos iz,i\sinh z=\sin iz.

sinh 、 cosh 和 tanh （就是双曲正弦、双曲余弦和双曲正切） sinh x = e x − e −x 2. cosh x = e x + e −x 2. tanh x = sinh x cosh x = e x − e −x e x + e −x. 导数. 这些函数的导数是： d dx sinh x = cosh x. d dx cosh x = sinh x. d dx tanh x = 1 − tanh 2 x

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.