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quasar987

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## Main Question or Discussion Point

I just got a clue as to why 0.5(e^x + e^-x) was called "hyperbolic cosine" and 0.5(e^x - e^-x) is called "hyperbolic sine". It is because the "complex version" reads

[tex]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/tex]

[tex]sin(x)=\frac{e^{ix}-e^{-ix}}{2i}[/tex]

That explains the "cos" and "sin" part in "cosh" and "sinh", but what does the "h" (hyperbolic) part comes from?

[tex]cos(x)=\frac{e^{ix}+e^{-ix}}{2}[/tex]

[tex]sin(x)=\frac{e^{ix}-e^{-ix}}{2i}[/tex]

That explains the "cos" and "sin" part in "cosh" and "sinh", but what does the "h" (hyperbolic) part comes from?