Difference between revisions of "Hyperbolic trig functions"

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The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows:
 
The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows:
<math>e^x+e^{-x}</math>
+
<math>\sinh{x}=\frac{e^x+e^{-x}}{2}</math>
 +
 
 +
<math>\cosh{x}=\frac{e^x-e^{-x}}{2}</math>
 +
 
 +
<math>\tanh{x}= \frac{\sinh{x}}{\cosh{x}} =\frac{e^x+e^{-x}}{e^x-e^{-x}}</math>
 +
 
 +
Also:
 +
 
 +
<math>\sinh{x}= -i\sin{ix}
 +
 
 +
</math>\cosh{x}=\cos{iz}
 +
 
 +
<math>\tanh{x}= -1\tan{iz}</math>
  
 
{{stub}}
 
{{stub}}

Revision as of 23:32, 22 May 2013

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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