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.

Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

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

\sinh \frac{x}{2}=\pm \sqrt{\frac{\cosh x-1}{2}}\left(\begin{array}{l} x>0, \qquad \text{取正号} \\ x<0,\qquad \text{取负号} \end{array} \right)\\ \cosh \frac{x}{2}=\sqrt{\frac{\cosh x+1}{2}} \\ \tanh \frac{x}{2}=\frac{\cosh x-1}{\sinh x}=\frac{\sinh x}{\cosh x+1} \\ \coth \frac{x}{2}=\frac{\sinh x}{\cosh x-1}=\frac{\cosh x+1}{\sinh x} \\

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.

The graphs and properties such as domain, range and asymptotes of the 6 hyperbolic functions: sinh(x), cosh(x), tanh(x), coth(x), sech(x) and csch(x) are presented. The six hyperbolic functions are defined as follows: Hyperbolic Sine Function : \( \sinh(x) = \dfrac{e^x - e^{-x}}{2} \)

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双曲正弦函数 sinh 和双曲余弦函数 cosh，从它们可以导出双曲正切函数 tanh 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。

2020年9月10日 · The cosh function is defined as: $$ \cosh{x} = \frac{e^{x}+e^{-x}}{2} $$ Here is a graph of the function: cosh as average of two exponentials. The cosh function can be interpreted as the average of two functions, $e^{x}$ and $e^{-x}$. This animation illustrates this: Other forms of …

2024年10月15日 · 在数学表达中，cosh函数定义为：cosh(x) = (e^x + e^(-x)) / 2。 这里的e是自然对数的底数，约等于2.71828。 这个公式表明，cosh函数是两个指数函数的和的一半。

1 cosh(x) The applet initially shows the graph of cosh( x ) on the left and its derivative on the right. The hyperbolic cosine looks sort of like a parabola, but looking at the derivative (which for a parabola is a straight line) you can see that the curvature isn't quite the same as a parabola.