Difference between revisions of "Hyperbolic trig functions"

Revision as of 22:33, 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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 The Hyperbolic trig functions can be thought of the classical trig functions except found on an unit hyperbola. There are as follows:
-<math>\sinh{x}=\frac{e^x+e^{-x}}{2}</math>
-<math>\cosh{x}=\frac{e^x-e^{-x}}{2}</math>
+<math>\sinh(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>
+<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>\sinh(x)= -i\sin{ix}</math>
+<math>\cosh(x)=\cos{iz}</math>
-</math>\cosh{x}=\cos{iz}
-<math>\tanh{x}= -1\tan{iz}</math>
+<math>\tanh(x)= -1\tan{iz}</math>
 {{stub}}