Hyperbolic Mnemonic

If you have problems remembering which is which with sinh and cosh, or their graphs, or which way around their definitions are:

\sinh x = \dfrac{\mathrm{e}^x - \mathrm{e}^{-x}}{2}

\cosh x = \dfrac{\mathrm{e}^x + \mathrm{e}^{-x}}{2}

then it might help if you notice that the graph of sinh is somewhat S-shaped (though backwards), and cosh is C-shaped (though open upwards).

[Well, unless you’re Russian, where the Cyrillic letter Es (‘С’) corresponds to our ‘S’; that might throw a graphemic spanner in the works.]

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