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#11. Hyperbolic Functions

和三角函數類似的, 有六個函數, 稱為hyperbolic function (雙曲函數), 其中兩個叫做hyperbolic sine 和hyperbolic cosine, 定義如下:.

#12. 6.9 Calculus of the Hyperbolic Functions - BC Open Textbooks

Apply the formulas for the derivatives of the inverse hyperbolic functions and their associated integrals. Describe the common applied conditions of a catenary ...

#13. 6.9: Calculus of the Hyperbolic Functions - Math LibreTexts

Hyperbolic functions are defined in terms of exponential functions. · Term-by-term differentiation yields differentiation formulas for the ...

#14. Hyperbolic functions

The hyperbolic sine. The domain: D(sinh) = ℝ. The graph: The function is continuous on its domain, unbounded, and symmetric, namely odd, since we have ...

#15. List of Hyperbolic Trigonometry Functions - Trig Identities

Hyperbolic Trig Identities is like trigonometric identities yet may contrast to it in specific terms. The fundamental hyperbolic functions are hyperbola sin ...

#16. Hyperbolic Functions - Properties, Derivatives, Graphs and ...

In Mathematics, hyperbolic functions are similar to trigonometric functions but are defined using the hyperbola rather than the circle.

#17. Hyperbolic Sine -- from Wolfram MathWorld

Abramowitz, M. and Stegun, I. A. (Eds.). "Hyperbolic Functions." §4.5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ...

#18. Hyperbolic Functions

Hyperbolic Functions. • sinh(z), cosh(z), tanh(z), csch(z), sech(z), coth(z)—Return the hyperbolic sine, cosine, tangent, cosecant, secant, and cotangent of ...

#19. 7.11 Inverse Hyperbolic Functions - CK-12

A function has an inverse if it is one-to-one. All of the hyperbolic functions except for \begin{align*}\text{cosh} \ x\end{align*} are ...

#20. Hyperbolic function - RDocumentation

These functions give the obvious hyperbolic functions. They respectively compute the hyperbolic cosine, sine, tangent, and their inverses, arc-cosine, ...

#21. Hyperbolic Trigonometric Functions - Maple Help - Maplesoft

Hyperbolic Functions Main Concept There are a total of six hyperbolic functions: Summary of the Hyperbolic Function Properties Name Notation Equivalence ...

#22. CC Hyperbolic Functions

Hyperbolic functions can be used to describe the shape of electrical lines freely hanging between two poles or any idealized hanging chain or cable supported ...

#23. Hyperbolic Functions - Meaning, Formulas, Examples, FAQs

Hyperbolic functions are defined analogously to trigonometric functions. We have main six hyperbolic functions, namely sinh x, cosh x, tanh x, coth x, sech x, ...

#24. Hyperbolic function definition and meaning - Collins Dictionary

Hyperbolic function definition: any of a group of functions of an angle expressed as a relationship between the distances... | Meaning, pronunciation ...

#25. Hyperbolic function Definition & Meaning | Dictionary.com

Hyperbolic function definition, a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to ...

#26. Hyperbolic functions - online Calculator - 123calculus.com

Hyperbolic functions · hyperbolic sine · hyperbolic cosine · hyperbolic tangent · hyperbolic cotangent · See also.

#27. Derivatives of Hyperbolic Functions - Math24.net

The basic hyperbolic functions are the hyperbolic sine function and the hyperbolic cosine function. They are defined as follows:.

#28. 6.4 Hyperbolic functions - Siyavula

Functions of the general form y=ax+q are called hyperbolic functions. Worked example 8: Plotting a hyperbolic function. y=h(x) ...

#29. 7.4 Hyperbolic Functions

1: Using trigonometric functions to define points on a circle and hyperbolic functions to define points on a hyperbola. These functions are sometimes referred ...

#30. Hyperbolic function Definition & Meaning - Merriam-Webster

The meaning of hyperbolic function is any of a set of six functions analogous to the trigonometric functions but related to the hyperbola in a way similar ...

#31. hyperbolic function - 雙曲函數 - 國家教育研究院雙語詞彙

中國大陸譯名: 双曲函数. 以hyperbolic function 進行詞彙精確檢索結果. 出處/學術領域, 英文詞彙, 中文 ...

#32. hyperbolic function - Wiktionary

EnglishEdit. NounEdit · hyperbolic function (plural hyperbolic functions). (mathematics) A set functions that are analogues of the trigonometric functions ...

#33. Hyperbolic functions Calculator - High accuracy calculation

Calculates the hyperbolic functions sinh(x), cosh(x) and tanh(x).

#34. 4.28 Definitions and Periodicity - DLMF

Relations to Trigonometric Functions ... As a consequence, many properties of the hyperbolic functions follow immediately from the corresponding ...

#35. Hyperbolic Functions (The GNU C Library)

These functions return the hyperbolic sine of x , defined mathematically as (exp ( x ) - exp (- x )) / 2 . They may signal overflow if x is too large. Function: ...

#36. Learning Hierarchical Representation for Functions of Source ...

Considering the inherent hierarchy of functions, we propose a novel hyperbolic function embedding (HFE) method, which can learn a distributed and ...

#37. Hyperbolic Trig Functions Graphs & Examples - Study.com

The hyperbolic functions take an area as their argument instead of an angle. · This is the graph of the hyperbolic sine function, sinh(x). · This ...

#38. definition of hyperbolic function by The Free Dictionary

n. Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the relationship of the ...

#39. Hyperbolic Functions: 9781490379845: McMahon, James

For instance, it has been customary to define the hyperbolic functions in relation to a sector of the rectangular hyperbola, and to take the initial radius ...

#40. NumPy ufuncs - Hyperbolic Functions - W3Schools

Hyperbolic Functions. NumPy provides the ufuncs sinh() , cosh() and tanh() that take values in radians and produce the corresponding sinh, cosh and tanh ...

#41. Hyperbolic Functions in the CATALOG

cosh-1( is the hyperbolic arccosine function. tanh-1( is the hyperbolic arctangent function. Each is valid for real numbers, expressions, and lists.

#42. The Extended Hyperbolic Function Method for Generalized ...

The extended hyperbolic function method is used to derive abundant exact solutions for generalized forms of nonlinear heat conduction and Huxley equations.

#43. Why Are Hyperbolic Functions Important? - Calculus

Why Are Hyperbolic Functions Important? ... Perhaps the best-known representation of a hyperbolic function is the Gateway Arch in St. Louis, MO (see image at ...

#44. hyperbolic function - WordReference.com Dictionary of English

hy′perbol′ic func′tion, [Math.] Mathematicsa function of an angle expressed as a relationship between the distances from a point on a hyperbola to the ...

#45. New complex and hyperbolic function solutions to the ...

In this study, we have applied the improved Bernoulli sub-equation function method to the generalized double combined Sinh-Cosh-Gordon ...

#46. Hyperbolic Functions - GeeksforGeeks

The hyperbolic cosine function is defined to be: cosh(x) = (e x + e -x )/2. And the hyperbolic sine function is defined as: Attention reader!

#47. LabTalk Programming - Trigonometric/Hyperbolic - OriginLab

Name Brief Example Acsch Return the inverse hyperbolic cosecant Example Asech Returns the inverse of the hyperbolic secant Example Asinh Returns the inverse hyperbolic sine Example

#48. hyperbolic functions - Wolfram|Alpha

hyperbolic functions. Natural Language; Math Input. NEWUse textbook math notation to enter your math. Try it. ×. Have a question about using Wolfram|Alpha?

#49. What is Hyperbolic Function? - A Plus Topper

It means that the relation which exists amongst cos θ, sin θ and unit circle, that relation also exist amongst cosh θ, sinh θ and unit hyperbola ...

#50. Hyperbolic Functions Formula: Equation of Hyperbola ... - Toppr

Hyperbolic functions refer to the exponential functions that share similar properties to trigonometric functions. These functions are analogous ...

#51. Hyperbolic functions – Graphs, Properties, and Examples

Hyperbolic functions are functions that parametrize a hyperbola. One of the most known examples of an object that can be modeled by a hyperbolic function is a ...

#52. (PDF) Note: hyperbolic function or equation of the hyperbola?

We will review concepts that are necessary to remember as hyperbolic, hyperbolic function graphs and hyperbolic functions.

#53. Hyperbolic function - Oxford Reference

A set of functions, sinh, cosh, and tanh, that have similar properties to trigonometric functions but are related to the hyperbola in the manner that ...

#54. Hyperbolic Functions - SOS Math

function (rhymes with the "Grinch") is depicted in blue. ... function is odd. Their most important property is their version of the Pythagorean ...

#55. Hyperbolic Functions - LabVIEW 2018 Help - Support

Use this class of elementary functions to compute hyperbolic functions and their inverses. The VIs on this palette can return mathematics error codes.

#56. Hyperbolic function - Wikipedia, the free encyclopedia

Contents · 1 Series definition · 2 Relationship to regular trigonometric functions · 3 Inverse hyperbolic functions · 4 Applications of inverse trigonometric ...

#57. Quantification of the relationship between insulin sensitivity ...

Evidence for a hyperbolic function. Diabetes. 1993 Nov;42(11):1663-72. doi: 10.2337/diab.

#58. Hyperbolic functions

Hyperbolic functions are analogues of the standard trigonometric functions. For each trig function there is an associated hyperbolic ...

#59. Six, hyperbolic function - DrHuang.com

Definition of hyperbolic functions, graphics and features. [ 双曲函数定义 ] [Hyperbolic function definition]. 函数 Function. 双曲正弦 Hyperbolic sine.

#60. Hyperbolic Trig Functions - MIT OpenCourseWare

So for hyperbolic trig functions we have the hyperbolic cosine and the hyperbolic sine. So the notation here, we write c o s h. So the ...

#61. Definition:Hyperbolic Function - ProofWiki

Definition. There are six basic hyperbolic functions, as follows: Hyperbolic Sine. The hyperbolic sine function is defined on the complex ...

#62. Symbolic hyperbolic sine function - MATLAB sinh - MathWorks

Examples. Hyperbolic Sine Function for Numeric and Symbolic Arguments. Depending on its arguments, sinh returns floating-point or exact symbolic results.

#63. Hyperbolic functions - Encyclopedia of Mathematics

The functions given by the formulas: sinhx=ex−e−x2,. the hyperbolic sine; and coshx=ex+e−x2,. the hyperbolic cosine.

#64. A Class of Analytic Functions associated with Sine Hyperbolic ...

We introduce a class of analytic functions subordinate to the function 1+\sinh \left( z\right) and obtain various necessary and sufficient ...

#65. Derivatives of inverse hyperbolic functions - Krista King Math

To build our inverse hyperbolic functions, we need to know how to find the inverse of a function in general. To find the inverse of a ...

#66. Hyperbolic functions — SymPy 0.7.4.1 documentation - omz ...

The hyperbolic cosine is an even, convex function with a global minimum at \(x = 0\), having a Maclaurin series that starts: >>> nprint(chop(taylor(cosh, 0, ...

#67. Best 3 Definitions of Hyperbolic-function - YourDictionary

What does hyperbolic-function mean? Any of a set of six functions related, for a real or complex variable x, to the hyperbola in a manner analogous to the r ...

#68. Hyperbolic Functions — Sage 9.4 Reference Manual

The full set of hyperbolic and inverse hyperbolic functions is available: hyperbolic sine: sinh(). hyperbolic cosine: cosh(). hyperbolic tangent: tanh().

#69. Hyperbolic Functions

mathematical applications (though much less commonly than our previous functions). Each hyperbolic function corresponds to a trigonometric function: to the ...

#70. 6.9 Calculus of the Hyperbolic Functions - OpenStax CNX

In this section, we look at differentiation and integration formulas for the hyperbolic functions and their inverses. Derivatives and Integrals ...

#71. Hyperbolic Functions Calculator

Hyperbolic functions calculator helps you calculate values of functions such as sinh, cosh, and tanh.

#72. hyperbolic function - Chinese translation – Linguee

Many translated example sentences containing "hyperbolic function" – Chinese-English dictionary and search engine for Chinese translations.

#73. Complex numbers and hyperbolic functions

in finding the roots of polynomial equations; and hyperbolic functions. 3.2 Manipulation of complex numbers. This section considers basic complex number ...

#74. What is a hyperbolic function? - Quora

Definition : a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, ...

#75. Spreadsheet: hyperbolic functions - MedCalc Software

Hyperbolic functions. SINH(x) Hyperbolic sine function. COSH(x) Hyperbolic cosine function. TANH(x) Hyperbolic tangent function.

#76. Why are the hyperbolic functions defined the way they are?

Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special relativity. Hyperbolic ...

#77. Hyperbolic Functions Table | Personal Criteria Formulas (PCF)

Hyperbolic functions are similar to the trigonometric functions (or circular functions) except that the points form the right half of the equilateral ...

#78. Hyperbolic Harmonic Functions and Hyperbolic Brownian ...

We study harmonic functions with respect to the Riemannian metric ... An important result is that a function f is \alpha -hyperbolic ...

#79. Simplifying exponential representation of hyperbolic functions ...

Applying .rewrite(sympy.cos) returns cosh(x) as you wanted. Apparently, the hyperbolic cosine is treated by rewrite as a variant of the ...

#80. Algebra II : Hyperbolic Functions - Varsity Tutors

Algebra II Help » Functions and Graphs » Quadratic Functions » Hyperbolic Functions ... Express the following hyperbolic function in standard form:.

#81. Graphs of Hyperbolic Functions - Free Mathematics Tutorials

Graphs of Hyperbolic Functions · Hyperbolic Sine Function : sinh(x)=ex−e−x2 · Hyperbolic Cosine Function : cosh(x)=ex+e−x2 · Hyperbolic Tangent Function : tanh( ...

#82. Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch

Hyperbolic Functions - sinh, cosh, tanh, coth, sech, csch. Definition of hyperbolic functions. Hyperbolic sine of x

#83. Hyperbolic Trig Functions (Explained w/ 15 Examples!)

Learn how to differentiate Hyperbolic Trig Functions and Inverse Hyperbolic Trig Functions with easy to follow steps, formulas, ...

#84. What does hyperbolic function mean? - Definitions.net

Hyperbolic functions occur in the solutions of some important linear differential equations, for example the equation defining a catenary, of some cubic ...

#85. Hyperbolic Functions

The other four trigonometric functions can then be defined in terms of cos and sin. Similarly, we may define hyperbolic functions coshα and sinhα from the “unit ...

#86. Intuitive Guide to Hyperbolic Functions - BetterExplained

The hyperbolic functions can be seen as exponential functions (relating time and growth) or geometric functions (relating area and coordinates). Hyperbolas, ...

#87. Hyperbolic Functions (video lessons, examples and solutions)

Hyperbolic Functions, Hyperbolic Identities, Derivatives of Hyperbolic Functions and Derivatives of Inverse Hyperbolic Functions, graphs of the hyperbolic ...

#88. 2 HYPERBOLIC FUNCTIONS

be able to find inverse hyperbolic functions and use them in calculus applications; ... The hyperbolic cosine function, written cosh x, is defined for all.

#89. 15.13. Limit of a Hyperbolic Function - Graphing Calculator by ...

A hyperbolic function are analogous to trigonometric functions but refer to base e. Below are six hyperbolic functions derived from the basic definitions of ...

#90. Exponential Functions vs. Trigonometric and Hyperbolic ...

Relations between exponential function and trigonometric/hyperbolic functions.

#91. Trigonometric and Hyperbolic Functions - Physics OER

which means that trigonometric and hyperbolic functions are closely related. Their behaviour as a function of x, however, is different: while sine and ...

#92. 3.10 Hyperbolic Trigonometric Functions - Stan

3.10 Hyperbolic Trigonometric Functions. R cosh (T x) hyperbolic cosine of x (in radians). R sinh (T x) hyperbolic sine of x (in radians). R tanh (T x)

#93. Category:Hyperbolic functions - Wikimedia Commons

This category has the following 10 subcategories, out of 10 total. C. Hyperbolic cosecant function‎ (1 C, 10 F).

#94. hyperbolic function in nLab

The hyperbolic functions (or sometimes hyperbolic trigonometric functions) are analogues of the usual trigonometric functions, ...

#95. Hyperbolic Functions - Desmos

a r c s i n h x. 3. c s c h x. 4. a r c c s c h x. 5. c o s h x. 6. a r c c o s h x. 7. 14. powered by. powered by. "x"$$ x. "y"$$ y. "a" squared$$ a 2.