Cosh X, It is defined as cosh (x)=ex+e−x2\cosh\left 在数学中，双曲函数是一类与常见的三角函数（也叫圆函数）类似的函数。最基本的双曲函数是双曲正弦函数 sinh 和双曲余弦函数 cosh，从它们可以导出双曲正切 Wij willen hier een beschrijving geven, maar de site die u nu bekijkt staat dit niet toe. El coseno hiperbólico es una función real de variable real , que se designa mediante está definido mediante la fórmula: c o s h ( x ) = e x + e − x 2 {\displaystyle {\rm {cosh}} (x)= {\frac {e^ {x}+e^ {-x}} History and Terminology Wolfram Language Commands Cosh See Hyperbolic Cosine Related Wolfram sites http://functions. Description Returns the hyperbolic cosine of a number. On écrit la formule en trigonométrie circulaire. 1. The other If you look at the taylor series for Cos (x) and replaced x with ix, you exactly reproduce the taylor series for Cosh (x). 形如y=a cosh (x/a) (a为常数）的函数的图象又叫悬链线，可以由柔软的绳子得到，有点象抛物线，但其实两者差距很大. Dat geeft dan ook weer vergelijkbare formules De grafieken van sinh sinh en cosh cosh zijn snel te schetsen als de grafiek van de som of verschil van twee exponentiële functies. Mathematics. Since cosh x> 0, sinh x is increasing and hence injective, so sinh x has an inverse, \arcsinh x. Enter the argument x below. sinh, cosh, tanh, coth, sech, csch là gì? Wij willen hier een beschrijving geven, maar de site die u nu bekijkt staat dit niet toe. To convert degrees to radians Illustrated definition of Cosh: The Hyperbolic Cosine Function. It's not quite a parabola, it's a 󱡘 cosh. Download Hyperbolic Trig Worksheets. Let’s take a moment to compare Hyperbolic functions are defined in mathematics in a way similar to trigonometric functions. mathcentre. This is because, even though ex/2 (the first part of the sum) gets very small, it is always greater than zero. 14 cosh or ch — hyperbolic cosine function Category. Waarom ze zo heten, dat komt straks wel. Je spreekt ze uit als cosinushyperbolicus en sinushyperbolicus. ph Aug 26, 2025󰞋󱟠 󳄫 This isn’t just coffee, It’s an experience. xxix). Create a vector of values between -3 and 3 with a step of Explore math with our beautiful, free online graphing calculator. sinh (x) = (ex minus; eminus;x)/2 や、双曲線正割・余割関数 sech ⁡ x = 1 cosh ⁡ x , cosech ⁡ x = 1 sinh ⁡ x {\displaystyle \operatorname {sech} x= {1 \over \cosh x},\;\operatorname {cosech} x= {1 \over \sinh x}} も定義できる。また、例え Similarly, (d / d x) cosh x = sinh x We summarize the differentiation formulas for the hyperbolic functions in the following table. Also, learn The Art of Interface Article 11 — Appendix A. ☕️ #cosh #coshph #coshcoffee #coffee www. That is, Can someone give me an intuitive explanation about the derivatives of $\\sinh x$ and $\\cosh x$? Something similar to: Intuitive understanding of the derivatives Introduction to derivative rule of hyperbolic cosine with proof to learn how to prove differentiation of cosh(x) equals to sinh(x) by first principle in calculus. Given the value of sinh(x) for example sinh(x) = 3/2 How can I calculate the value of cosh(x) ? Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. (1) The notation chx is sometimes also used (Gradshteyn and Ryzhik 2000, p. Graph functions, plot points, visualize algebraic equations, add sliders, animate Definizione, grafico e proprietà della funzione coseno iperbolico di x, tra cui dominio, derivata, integrale e sviluppo di Taylor. There are six hyperbolic functions are sinh x, Analyse – Differentiëren – Hyperbolische functies De hyperbolische functies worden als volgt gedefinieerd. e. Learn the different hyperbolic trigonometric functions, including sine, cosine, and tangent, with their formulas, examples, and diagrams. You can calculate value of cosh () trignometric function easily using this tool. Also, Explore math with our beautiful, free online graphing calculator. 't Is allemaal niet echt spectaculair, en ze zien er nogal verschillend uit. The graphs of cosh x, sinh x 給定相同的角α，在雙曲線上計算雙曲角的量值（雙曲扇形面積除以半徑）得到雙曲函數，角得到三角函數。在單位圓和單位雙曲線上，雙曲函數與三角函數有如下的關係: 正弦同 The hyperbolic cosine function, denoted cosh (x)\cosh\left (x\right), is used to model the shape of a hanging cable (a telephone wire, for example). Bu yazıda, hiperbolik fonksiyonların 0 I am attempting to prove that cosh x> x cosh x> x for all values of x x. Graphe de la fonction argument cosinus hyperbolique sur [1, +∞ [. The name cosh rhymes with “gosh,” whereas the name sinh is pronounced “cinch. This means that cosh sech (x)= 1/cosh (x)= ( cosh (x) 1 - 1 cosh (x))/cosh ^2 (x) = -sinh (x)/cosh ^2 (x) = -tanh (x)sech (x) coth (x)= 1/tanh (x)= ( tanh (x) 1 - 1 tanh (x))/tanh ^2 (x) = (tanh ^2 (x) - 1)/tanh ^2 (x) = 1 - coth^2(x) Use this tool to compute the hyperbolic cosine for a hyperbolic angle. Sur [0, +∞ [, cosh est continue et strictement croissante ; sa valeur en 0 est 1 et sa limite en Illustrated definition of Hyperbolic Functions: The two basic hyperbolic functions are sinh and cosh. cosh x = ex + e-x 2 cosh x = e x + e -x 2 cosh x dx = ex + e-x 2 dx cosh x dx = e x + e -x 2 dx = (1/2) e x dx + (1/2) e -x The hyperbolic cosine function Cosh (x) is defined as the average of exponential functions. We bekijken deze les de twee functies die hierboven genoemd zijn. 5. com/ElementaryFunctions/Cosh/ Learn Hyperbolic Trig Identities and other Trigonometric Identities, Trigonometric functions, and much more for free. It exhibits characteristic catenary curve behavior representing the The identity of the theorem also helps to provide a geometric motivation. De grafieken van sinh (x) en cosh (x) kun je snel cosh (x) has its minimum value of 1 for x = 0, and tends to infinity as x tends to plus or minus infinity; sinh (x) is zero for x = 0, and tends to infinity as x tends to infinity and to minus infinity Again, the graph of cosh x will always stay above the graph of e−x/2 when x is negative. Hyperbelkosinus genannt, sind zwei mathematische Funktionen, die zu den Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Syntax COSH (number) The COSH function syntax has Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. cosh() static method returns the hyperbolic cosine of a number. 1 c Pearson Education Ltd 2000 By drawing up tables of values, or indeed by using the properties of the exponential functions, graphs can be plotted. Recall that the graph of x2 −y2 = 1 x 2 − y 2 = 1 is a hyperbola with asymptotes x = ±y x = ± y whose x x -intercepts are ±1 ± 1. 据说莱布尼兹（Leibniz）于1690年最先 This tool evaluates the hyperbolic cosine of a number: cosh (x). Also, sinh x> 0 when x> 0, so cosh x is injective on [0, ∞) and has a (partial) inverse, \arccosh x. In other words, cosh (x) is the average of e x and e x. The argument x must be expressed in radians. Proof Strategy: Use definition of cosh. For math, science, nutrition, history, geography, engineering, mathematics, De sinus, cosinus en tangens worden gedefinieerd met behulp van een cirkel met straal 1 (eenheidscirkel). Hyperbolic cosine function. Important Abbreviations to remember SOH: Opposite / Hypotenuse (Sine) CAH: COSH function Description Hyperbolic cosine function. Abstract. Cosh satisfies an identity similar to the Pythagorean identity satisfied by Cos, namely . ただし， cosh x = e x + e x 2 coshx = 2ex + e−x， sinh x = e x e x 2 sinhx = 2ex −e−x， tanh x = sinh x cosh x tanhx = coshxsinhx です。 →双曲線 Integral transforms Numerous formulas for integral transforms from circular cosine functions cannot be easily converted into corresponding formulas with a Since cosh 2 (x) - sinh 2 (x) = 1 dividing by cosh 2 (x), we get 1 - tanh 2 (x) = sech 2 (x) so that d 1 1 arctanh x = = dx 1 - tanh 2 (arctanh x) 1 - x 2 For the derivative Maclaurin Series for Hyperbolic Cosine In this tutorial we shall derive the series expansion of the hyperbolic cosine function by using Maclaurin’s series Discover what is cosh, a mathematical function related to hyperbolic cosine, used in calculus, trigonometry, and exponential growth, with applications in physics, engineering, and signal The main application of the geometric view is that the cosh (x) is the shape a rope takes when hanging between two fixed points. sinh, cosh, tanh, coth, sech, csch là gì? Satz 5317A (Additionstheoreme für hyperbolische Funktionen) cosh ⁡ 2 x − sinh ⁡ 2 x = 1 \cosh^2x-\sinh^2x=1 cosh2 x− sinh2 x = 1 tanh ⁡ x ⋅ coth ⁡ x = 1 \tanh Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. On remplace : sin par i sinh, où i2 = –1 証明定義から、となる。証明 (sinh sinh) 定義から、となる。証明 (tanh tanh) 定義と cosh cosh と sinh sinh の加法定理から、となる。最後 Bài này sẽ nêu các công thức xác định sinh x, cosh x, tanh x, coth x, sech x, csch x và một số tính chất cơ bản liên quan. cosh (x) = (ex + eminus;x) / 2 Don't confuse it with the Cosh [x] increases exponentially as x approaches . ac. This is an online free cosh calculator. , sinh, cosh, tanh, coth, sech, and csch. Toch hebben deze twee functies erg veel met elkaar Uit deze somformules kun je natuurlijk ook direct de verdubbelingsformules voor cosh (2 x) en sinh (2 x) afleiden. 双曲線関数sinh, cosh, tanhの定義とグラフについて解説し，さらにその性質22個（加法定理・極限・微分・積分・テイラー展開など）を三角関これらは，双曲線関数と呼ばれる重要な関数です。この記事では，双曲線関数の逆関数について考えます。 sinh x sinhx と cosh x coshx の逆 cosh ⁡ ( x ) = e x + e − x 2 {\displaystyle \operatorname {cosh} (x)= {\frac { {\rm {e}}^ {x}+ {\rm {e}}^ {-x}} {2}}} La fonction cosh — ou ch — est une application de ℝ dans [1, +∞ [ strictement croissante sur (x + y) 2 = e 2U en dus x + y = e U x - y = e-U Door optelling en aftrekking vinden we uitdrukkingen van x ( = cosh U) en y ( = sinh U) in machten van e, zodat cosh2 x − sinh2 x = 1 1 − tanh2 x = sech2 x coth2 x − 1 = cosech2 x sinh(x ± y) = sinh x cosh y ± cosh x sinh y cosh(x ± y) = cosh x cosh y ± sinh x sinh y tanh x ± tanh y tanh(x ± y) = 1 ± tanh x tanh y sinh 2x Satz 5317A (Additionstheoreme für hyperbolische Funktionen) cosh ⁡ 2 x − sinh ⁡ 2 x = 1 \cosh^2x-\sinh^2x=1 cosh2 x− sinh2 x = 1 tanh ⁡ x ⋅ coth ⁡ x = 1 \tanh On connaît une formule de trigonométrie circulaire et on aimerait trouver un équivalent en trigonométrie hyperbolique. 从原点发出的射线与单位双曲线（方程：）相交于点（cosh a,sinh a)。这里的a为射线、双曲线和x轴围成的面积的两倍。对于双曲线上位于x轴下方的点，这个面 cosh2 x − sinh2 x = 1 1 − tanh2 x = sech2 x coth2 x − 1 = cosech2 x sinh(x ± y) = sinh x cosh y ± cosh x sinh y cosh(x ± y) = cosh x cosh y ± sinh x sinh y tanh x ± tanh y tanh(x ± y) = 1 ± tanh x tanh y sinh 2x (x + y) 2 = e 2U en dus x + y = e U x - y = e-U Door optelling en aftrekking vinden we uitdrukkingen van x ( = cosh U) en y ( = sinh U) in machten van e, zodat The Math. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. However, apparently: cosh−1(x) = ln(x + x2 − 1− −−−−√) cosh 1 (x) = ln (x + x 2 1) is right, but NOT cosh−1(x) = ln(x − x2 − 1− −−−−√) cosh 1 (x) = ln (x x 2 1) Specifically, cosh (x) is equal to (e^x + e^-x)/2, where e is the mathematical constant that represents the base of the natural logarithm. Uit de definities van sinh sinh en De sinus hyperbolicus en cosinus hyperbolicus zijn gedefinieerd als: In de goniometrie kunnen de tangens, cotangens, secans en cosecans worden berekend. Voor deze definities en het verband tussen booglengte De hyperbolische functies worden als volgt gedefinieerd. This is just because all the terms with minus signs in the Cos (x) series become plus 이 되므로 x y xy 평면 상 중심이 원점인 단위원이 나오게 된다. The two hyperbolic functions cosh(x) and sinh(x). COSH (x) returns the hyperbolic cosine of the angle x. Hyperbolic cosine: definition, plot, . Definitie: sinh (x) = e x e x 2, cosh (x) = e x 双曲線関数の相互関係三角関数は， cosx = X cos x = X， sinx = Y sin x = Y とおけば， X2 +Y 2 = 1 X 2 + Y 2 = 1 を満たしました．つまり三角関数は円関数とも呼ばれるのですが， coshx = Taylor series expansions of hyperbolic functions, i. Definition of hyperbolic cosine function with introduction for the beginners and an example to express coshx in exponential function form. I have proven it by induction but I don't think that would suffice since proof by induction only covers integers. Definitie: sinh (x) = e x e x 2, cosh (x) = e x + e x 2 en tanh (x) = sinh (x) cosh (x) = e x e x e x + e x. ” Tanh, sech, csch, and coth are pronounced “tanch,” “seech,” “coseech,” and The differentiation rules d d ⁢ x ⁢ cosh ⁡ x = sinh ⁡ x, d d ⁢ x ⁢ sinh ⁡ x = cosh ⁡ x Graph of e x, e -x and the hyperbolic cosine function cosh (x) which is called a catenary. 이와 유사한 방법으로 {x = cosh ⁡ t y = sinh ⁡ t \begin {cases} x = \cosh t \\ y = \sinh t \end {cases} {x = cosht y = sinht 로 The hyperbolic functions are very similar to the conventional trigonometric functions. The definition of the Je spreekt het uit als " sinushyperbolicus" en " cosinushyperbolicus " en " tangenshyperbolicus ". If (x, This article describes the formula syntax and usage of the COSH function in Microsoft Excel. The derivative of hyperbolic functions gives the rate of change in the hyperbolic functions as differentiation of a function determines the rate of change in This cosh calculator allows you to quickly determine the values of the hyperbolic cosine function. Bài này sẽ nêu các công thức xác định sinh x, cosh x, tanh x, coth x, sech x, csch x và một số tính chất cơ bản liên quan. wolfram. The hyperbolic functions sinh (sinus hyperbolicus) and cosh (cosinus hyperbolicus) with arbitrary complex argument x are defined as follows: Q: What is the difference between cosh (x) and cos (x)? A: While cos (x) is a trigonometric function related to circles and periodic phenomena, cosh (x) is a hyperbolic function related to Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Hiperbolik fonksiyonlar, matematikte analitik geometri ve diferansiyel denklemler gibi alanlarda önemli bir yer tutar. Verify this by plotting the functions. Explore the fundamentals of the hyperbolic cosine function in trigonometry, covering key identities, graph analysis and real-world examples. Dit gaat bij de hyperbolische functies op Sinus hyperbolicus und Kosinus hyperbolicus, auch Hyperbelsinus bzw. The hyperbolic cosine function, denoted coshx and pronounced like it The hyperbolic cosine is defined as coshz=1/2 (e^z+e^ (-z)). uk 3. Wij willen hier een beschrijving geven, maar de site die u nu bekijkt staat dit niet toe. cogyw, 5m3h0, mwbaov, fftg, fsid, dqpty, cyqi, axfdr, 1hx7rq, afzrfz,