The hyperbolic functions are defined as follows:
The graphs of hyperbolic functions are below:
From these graphs, the domain and range of the hyperbolic functions can be found:
The inverse hyperbolic functions are
The domains and ranges can be found:
The inverse hyperbolic functions have logarithmic forms that can be proved by using the exponential definition of the hyperbolic functions and solving the hidden quadratic. These are:
The most important hyperbolic identity is:
When proving identities, it is often useful to return to the exponential definitions of
The derivatives of hyperbolic functions are:
The integrals of hyperbolic functions are: