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* <math>tan(x) = \frac{sinh(x)}{cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}}</math> | * <math>tan(x) = \frac{sinh(x)}{cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}}</math> | ||
| − | * | + | * <math>coth(x) = \frac{cosh(x)}{sinh(x)} = \frac{{e^x + e^{-x}}}{{e^x - e^{-x}}}</math> |
| + | |||
| + | * <math>sech(x) = \frac{1}{cosh(x)} = \frac{1}{{e^x + e^{-x}}}</math> | ||
| + | |||
| + | * <math>csch(x) = \frac{1}{sinh(x)} = \frac{1}{{e^x - e^{-x}}{2}}</math> | ||
Revision as of 15:08, 11 October 2008
Just in case you don't have to look them up in your book or whatever. And so I can learn how to use Latex!
Hyperbolic Functions
- $ sinh(x) = \frac{e^x - e^{-x}}{2} $
- $ cosh(x) = \frac{e^x + e^{-x}}{2} $
- $ tan(x) = \frac{sinh(x)}{cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}} $
- $ coth(x) = \frac{cosh(x)}{sinh(x)} = \frac{{e^x + e^{-x}}}{{e^x - e^{-x}}} $
- $ sech(x) = \frac{1}{cosh(x)} = \frac{1}{{e^x + e^{-x}}} $
- $ csch(x) = \frac{1}{sinh(x)} = \frac{1}{{e^x - e^{-x}}{2}} $
