Hyperbolic Functions

In this post we define Hyperbolic  Functions and also discuss their domains and ranges. The  hyperbolic Functions have same properties that resembles to those of trigonometric functions.

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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