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The graph of the function a cosh(x/a) is the catenary, the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.

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

$\text{cosh}(x \pm y) = \text{cosh}\ x\ \text{cosh}\ y \pm \text{sinh}\ x\ \text{sinh}\ y$ $\text{tanh}(x \pm y) = \frac{\text{tanh}\ x \pm \text{tanh}\ y}{1 \pm \text{tanh}\ x \cdot \text{tanh}\ y}$ $\text{coth}(x \pm y) = \frac{\text{coth x}\ \text{coth}\ y \pm l}{\text{coth}\ y \pm \text{coth}\ x}$

Graphs of Hyperbolic Functions. 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 : \( \sinh(x) = \dfrac{e^x - e^{-x}}{2} \)

COSH (x) returns the hyperbolic cosine of the angle x. The argument x must be expressed in radians. To convert degrees to radians you use the RADIANS function. The argument x can be a real number, a complex number, or a matrix.

Sep 10, 2020 · Equation and graph. 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 the equation

Use the definition of cosh: cosh(0) = (exp(0) + exp(-0))/2 = 2 / 2 = 1. Use the identity cosh 2 x − sinh 2 x = 1 along with the fact that sinh is an odd function, which implies sinh(0) = 0. Read the answer from the graph of the hyperbolic cosine function. Use an online cosh calculator.

The calculator will draw the graph of the function $$$ y = f{\left(x \right)} = \cosh{\left(x \right)} $$$. To draw a parabola, circle, ellipse or hyperbola, choose the "Implicit" option.

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