what does arcsinh mean Definitions sinh cosh and tanh csch sech and coth There are various equivalent ways to define the hyperbolic functions Exponential definitions sinh x is half the difference of e x and e x cosh x is the average of e x and e x In terms of the exponential function Hyperbolic sine the odd part of the exponential function that is Hyperbolic
The inverse hyperbolic sine sinh 1 z Beyer 1987 p 181 Zwillinger 1995 p 481 sometimes called the area hyperbolic sine Harris and Stocker 1998 p 264 is the multivalued function that is the inverse function of the hyperbolic sine The variants Arcsinhz or Arsinhz Harris and Stocker 1998 p 263 are sometimes used to refer to explicit Arcsinh x Natural Language Math Input Extended Keyboard Examples Upload Random Compute answers using Wolfram s breakthrough technology knowledgebase relied on by millions of students professionals For math science nutrition history geography engineering mathematics linguistics sports finance music
what does arcsinh mean
what does arcsinh mean
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What Is Arcsin Formula Graph Domain And Range Examples Arcsin x
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What Is Arcsin Visual Fractions
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Several notations for the inverse trigonometric functions exist The most common convention is to name inverse trigonometric functions using an arc prefix arcsin x arccos x arctan x etc This convention is used throughout this article This notation arises from the following geometric relationships citation needed when measuring in In order to invert the hyperbolic cosine function however we need as with square root to restrict its domain By convention cosh 1 x is taken to mean the positive number y such that x cosh y This function is shown in red in the figure notice that cosh 1 x is defined only for x ge 1 at least where real numbers are concerned
See Inverse Hyperbolic Sine Related Wolfram sites functions wolfram ElementaryFunctions ArcSinh ArcSinh z gives the inverse hyperbolic sine sinh 1 z of the complex number z
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The function y sin 1 x Next we define the inverse sine function For this we again first recall the graph of the y sin x function and note that it is also not one to one However when restricting the sine to the domain left dfrac pi 2 dfrac pi 2 right the restricted function is one to one Note furthermore that when restricting the domain ArcSinh z 2442 formulas ArcSinh Visualizations 223 graphics 1 animation Plotting Evaluation Elementary Functions ArcSinh z 2442 formulas Primary definition 1 formula Specific values 32 formulas General characteristics 13 formulas
The inverse hyperbolic sine function in modern notation written as arsinh t or arcsinh t or sinh 1 t gives the value x hyperbolic angle so that The inverse hyperbolic sine function accepts arguments from the whole real space Since the hyperbolic sine is defined through the natural exponential function For example x 1 means 1 x but sin 1 x does not mean 1 sin x Doctor Vogler answered Hi Anthony Thanks for writing to Dr Math That s a good question When you raise a function to the 1 power what does that mean The short answer is that it means the inverse but unfortunately there are at least two meanings for that
SOLVED 5 Differentiate Y Sinh ln x Y Arctan sin x Y Arcsinh
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what does arcsinh mean - In order to invert the hyperbolic cosine function however we need as with square root to restrict its domain By convention cosh 1 x is taken to mean the positive number y such that x cosh y This function is shown in red in the figure notice that cosh 1 x is defined only for x ge 1 at least where real numbers are concerned