Hyperbolic sine, denoted as $$ ext{sinh}(x)$$, is a mathematical function defined as $$ ext{sinh}(x) = \frac{e^x - e^{-x}}{2}$$. This function is one of the key hyperbolic functions that arise in various areas of mathematics, including geometry and complex analysis, and it has properties that resemble those of the sine function but relate to hyperbolas rather than circles. Understanding hyperbolic sine helps in solving equations related to hyperbolic geometry and also connects with exponential functions in calculus.
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