Difference between revisions of "Hyperbolic trig functions"

 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
 
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>
 +
 
 +
 
 +
<math>\cosh(x)=\cos{iz}</math>
 +
 
 +
 
 +
<math>\tanh(x)= -1\tan{iz}</math>
  
 
{{stub}}
 
{{stub}}

Latest revision as of 23:33, 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:

$\sinh(x)= -i\sin{ix}$


$\cosh(x)=\cos{iz}$


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

This article is a stub. Help us out by expanding it.

Invalid username
Login to AoPS