Hyperbolic Functions

This exploration delves into the realm of Hyperbolic Functions, outlining their definitions, domains, and ranges. Notably, these functions exhibit intriguing parallels to their trigonometric counterparts, sharing a set of analogous properties.

Functions                       Formulas

y = Sinh x

\frac{e^x-e^{-x}}{2}, Domain=Range=R

y = Cosh x

\frac{e^x+e^{-x}}{2}, Domain=R , Range=[1,+\infty)

y = Tanh x

   \frac{e^x-e^{-x}}{e^x+e^{-x}}

y = Coseh x

 \frac{2}{e^x+e^{-x}}

y = Sech x

  \frac{2}{e^x-e^{-x}}

y = Coth x

  \frac{e^x+e^{-x}}{e^x-e^{-x}}

 

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