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If x = sinh y, then y = sinh-1 a is called the inverse hyperbolic sine of x. Similarly we define the other inverse hyperbolic functions. The inverse hyperbolic functions are multiple-valued and as in the case of inverse trigonometric functions we restrict ourselves to principal values for which they can be considered as single-valued.
10 Ιουλ 2024 · This sinh calculator allows you to quickly determine the values of the hyperbolic sine function.
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The value of the hyperbolic functions sinh and cosh in the point 0 of the x-axis is, thanks to the properties of the exponential function, the same as the "normal trigonometric functions": The value of the hyperbolic sine is: sinh(0) = 0. The value of the hyperbolic cosine is: cosh(0) = 1.
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.
The hyperbolic sine function, \sinh x, is one-to-one, and therefore has a well-defined inverse, \sinh^{-1} x, shown in blue in the figure. In order to invert the hyperbolic cosine function, however, we need (as with square root) to restrict its domain.
Hyperbolic Definitions sinh(x) = ( e x - e-x)/2 . csch(x) = 1/sinh(x) = 2/( e x - e-x) . cosh(x) = ( e x + e-x)/2 . sech(x) = 1/cosh(x) = 2/( e x + e-x) . tanh(x ...
