Hyperbolic trig functions

The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows: $\sinh{x}=\frac{e^x+e^{-x}}{2}$

$\cosh{x}=\frac{e^x-e^{-x}}{2}$

$\tanh{x}= \frac{\sinh{x}}{\cosh{x}} =\frac{e^x+e^{-x}}{e^x-e^{-x}}$

Also:

$\sinh{x}= -i\sin{ix}$\cosh{x}=\cos{iz}

$\tanh{x}= -1\tan{iz}$

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