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Definitions of hyperbolic sine:
  • noun:   (mathematics) A hyperbolic function that is the analogue of the sine function for hyperbolic spaces, taking in a hyperbolic angle as an argument and returning the y-coordinate for the corresponding point on the unit hyperbola. It is written in symbol sinh and can be represented as: sinh (x)= tfrac 1 2(eˣ-e⁻ˣ)

(Definitions from Wiktionary)

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