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 : \( \sinh(x) = \dfrac{e^x - e^{-x}}{2} \)
The graph of \( y = \sinh(x) \) is shown below along with the graphs of \( y = \dfrac{e^x}{2} \) and \( y = - \dfrac{e^{-x}}{2} \) for comparison
Domain: \( (-\infty , \infty) \)
Range: \( (-\infty , \infty) \)
Odd function: \(\sinh(-x) = - \sinh(x) \)
The graph of \( y = \cosh(x) \) is shown below along with the graphs of \( y = \dfrac{e^x}{2} \) and \( y = \dfrac{e^{-x}}{2} \) for comparison
Domain: \( (-\infty , \infty) \)
Range: \( [1 , \infty) \)
Even function: \(\sinh(-x) = \sinh(x) \)