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You can find numerous equivalent means for defining the hyperbolic features. They may be outlined with regard to the exponential perform:
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It might be demonstrated go that the region under the curve of cosh (x) over a finite interval is often equal on the arc length similar to that interval:[twelve]
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tanh x = sinh x cosh x = e x − e − x e x + e − x = displaystyle tanh x= frac find more information sinh x cosh x = frac e^ x -e^ -x e^ x +e^ -x =
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These expressions are analogous towards the expressions for sine and cosine, dependant on Euler's formula, as sums of complex exponentials.
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