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sinh (x)/cosh (x), valid input values range from -1 to 1. 1/cosh (x), valid input values range from 0 to 1. This sinh calculator allows you to quickly determine the values of the hyperbolic sine function.

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Inverse hyperbolic functions. 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.

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.

可见，双曲正弦函数的二阶导数仍然是双曲正弦函数（它本身），而根据双曲正弦函数的 单调性 ，且sinh0=0。可知当x>0时，sinhx的二阶导数大于0。x<0时，sinhx的二阶导数小于0，则可得出上述结论。

sinh (x) = ex − e-x 2. cosh (x) = ex + e-x 2. They use the natural exponential function ex. And are not the same as sin (x) and cos (x), but a little bit similar: One of the interesting uses of …