All capabilities with this house are linear combos of sinh and cosh, in particular the exponential features e x displaystyle e^ x

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ery, kosh′ėr-i, n. The traditional proper of the Irish chief to quarter himself and his retainers on his tenantry—also cosh

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The size of a hyperbolic angle is twice the realm of its hyperbolic sector. The hyperbolic features can be described regarding the legs of the suitable triangle masking this sector.

The function cosh x features a Taylor series expression with only even exponents for x. Consequently it really is a fair functionality, that may be, symmetric with regard into the y-axis. The sum of the sinh and cosh collection could be the infinite sequence expression with the exponential functionality.

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coth x = cosh x sinh x = e x + e − x e x − e − x = displaystyle coth x= frac cosh x sinh x = frac e^ x +e^ -x e^ x -e^ -x =

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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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