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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.
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10 Ιουλ 2024 · This sinh calculator allows you to quickly determine the values of the hyperbolic sine function.
It is a tool that computes the values of six basic hyperbolic functions – sinh, cosh, tanh, coth, sech, and csch – all in a blink of an eye. You can also use it to calculate the inverse hyperbolic functions.
In the points z=2 pnä’m’;n˛Zìm˛Z, the values of the hyperbolic functions are algebraic. In several cases, they can even be rational numbers, 1, or ä (e.g. sinhHpä’2L=ä, sechH0L=1, or coshHpä’3L=1’2). They can be expressed using only square roots if n˛Z and m is a product of a power of 2 and distinct Fermat primes {3, 5, 17 ...
d y d x = 1 cosh y = 1 1 + sinh 2 y = 1 1 + x 2. d y d x = 1 cosh y = 1 1 + sinh 2 y = 1 1 + x 2. We can derive differentiation formulas for the other inverse hyperbolic functions in a similar fashion.
Definition 4.11.1 The hyperbolic cosine is the function coshx = ex + e − x 2, and the hyperbolic sine is the function sinhx = ex − e − x 2. . Notice that cosh is even (that is, cosh(− x) = cosh(x)) while sinh is odd (sinh(− x) = − sinh(x)), and coshx + sinhx = ex.
