Hyperbolic trigonometric functions

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sinh (x) = \frac{e^{x} - e^{- x}}{2}

cosh (x) = \frac{e^{x} + e^{- x}}{2}

tanh (x) = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}} = \frac{sinh (x)}{cosh (x)}

sech (x) = \frac{2}{e^{x} + e^{- x}} = \frac{1}{cosh (x)}

csch (x) = \frac{2}{e^{x} - e^{- x}} = \frac{1}{sinh (x)}

coth (x) = \frac{e^{x} + e^{- x}}{e^{x} - e^{- x}} = \frac{cosh (x)}{sinh (x)} = \frac{1}{tanh (x)}

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Made with ASCIIsvg by Peter Jipsen, Chapman University, January 2005