The cosh function is a hyperbolic function. It is also known as the hyperbolic cosine function.
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
If we multiply the top and bottom of the original equation for the cosh function by $e^{x}$ we get:
$$ \sinh{x} = \frac{e^{2x}+1}{2e^{x}} $$
Alternatively, if we multiply the top and bottom of the original equation for the cosh function by $e^{-x}$ we get:
$$ \sinh{x} = \frac{1+e^{-2x}}{2e^{-x}} $$
These alternative forms are sometimes useful.
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