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==Hyperbolic Functions== | ==Hyperbolic Functions== | ||
| − | * <math>sinh(x) = \frac{e^x - e^{-x}}{2}</math> | + | * <math>\sinh(x) = \frac{e^x - e^{-x}}{2}</math> |
| − | * <math>cosh(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> | + | * <math>\tanh(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>\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{2}{{e^x + e^{-x}}}</math> | + | * <math>\text{sech}(x) = \frac{1}{\cosh(x)} = \frac{2}{{e^x + e^{-x}}}</math> |
| − | * <math>csch(x) = \frac{1}{sinh(x)} = \frac{2}{e^x - e^{-x}}</math> | + | * <math>\text{csch}(x) = \frac{1}{\sinh(x)} = \frac{2}{e^x - e^{-x}}</math> |
[[User:Idryg|Idryg]] 20:10, 11 October 2008 (UTC) | [[User:Idryg|Idryg]] 20:10, 11 October 2008 (UTC) | ||
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==Basic Integration Formulas== | ==Basic Integration Formulas== | ||
| − | <math>\int\frac{du}{\sqrt{a^2-u^2}}=sin^{-1}\frac{u}{a} + C</math> | + | <math>\int\frac{du}{\sqrt{a^2-u^2}}=\sin^{-1}\frac{u}{a} + C</math> |
Revision as of 10:50, 12 October 2008
Just in case so 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} $
- $ \tanh(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}}} $
- $ \text{sech}(x) = \frac{1}{\cosh(x)} = \frac{2}{{e^x + e^{-x}}} $
- $ \text{csch}(x) = \frac{1}{\sinh(x)} = \frac{2}{e^x - e^{-x}} $
Idryg 20:10, 11 October 2008 (UTC)
Basic Integration Formulas
$ \int\frac{du}{\sqrt{a^2-u^2}}=\sin^{-1}\frac{u}{a} + C $
