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These expressions are analogous into the expressions for sine and cosine, dependant on Euler's formula, as sums of advanced exponentials.

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You can find different equivalent methods for defining the hyperbolic functions. They could be outlined when it comes to the exponential function:

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Duplicate the instance facts in the following table, and paste it in mobile A1 of a new Excel worksheet. For formulas to point out outcomes, decide on them, press F2, after which push Enter. If you have to, you may adjust the column widths to find out all the info.

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tanh ⁡ x = sinh ⁡ x cosh ⁡ x = e x − e − x e x + e − x = displaystyle tanh x= frac sinh x cosh x = frac e^ x -e^ -x e^ x +e^ -x =

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