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Hyperbolic trigonometric functions (view source)
Revision as of 01:03, November 16, 2008
, 01:03, November 16, 2008New page: The '''hyperbolic trigonometric functions''' are analogs of the standard trigonometric functions using a hyperbola rather than a circle. They are defined as: *Hyperbolic sine: <math>sinh...
The '''hyperbolic trigonometric functions''' are analogs of the standard trigonometric functions using a hyperbola rather than a circle. They are defined as:
*Hyperbolic sine: <math>sinh(x) = \frac{e^x - e^{-x}}{2}</math>
*Hyperbolic cosine: <math>cosh(x) = \frac{e^x + e^{-x}}{2}</math>
*Hyperbolic tangent: <math>tanh(x) = \frac{sinh(x)}{cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}}</math>
*Hyperbolic cosecant: <math>csch(x) = \frac{1}{sinh(x)} = \frac{2}{e^x - e^{-x}}</math>
*Hyperbolic secant: <math>sech(x) = \frac{1}{sinh(x)} = \frac{2}{e^x + e^{-x}}</math>
*Hyperbolic tangent: <math>coth(x) = \frac{cosh(x)}{sinh(x)} = \frac{e^x + e^{-x}}{e^x - e^{-x}}</math>
[[Category:Mathematics]]
*Hyperbolic sine: <math>sinh(x) = \frac{e^x - e^{-x}}{2}</math>
*Hyperbolic cosine: <math>cosh(x) = \frac{e^x + e^{-x}}{2}</math>
*Hyperbolic tangent: <math>tanh(x) = \frac{sinh(x)}{cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}}</math>
*Hyperbolic cosecant: <math>csch(x) = \frac{1}{sinh(x)} = \frac{2}{e^x - e^{-x}}</math>
*Hyperbolic secant: <math>sech(x) = \frac{1}{sinh(x)} = \frac{2}{e^x + e^{-x}}</math>
*Hyperbolic tangent: <math>coth(x) = \frac{cosh(x)}{sinh(x)} = \frac{e^x + e^{-x}}{e^x - e^{-x}}</math>
[[Category:Mathematics]]