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How To Use Hyperbolic In A Sentence

  • Clearly the megalosaurus in the opening passage of Bleak House is a flight of hyperbolic fancy (inspired, I would guess, by the papier-mâché dinosaurs constructed for the Crystal Palace Exhibition, a couple of years earlier).
  • The authors, both pollsters, will either win plaudits in future years or be forgotten like many hyperbolic, wrong-headed forecasters through the eons. Three books on the Tea Party, reviewed by Steven Levingston
  • A corollary to Godwin's Law, and as much of a thread quasher, must be hyperbolic reference to Mandela, Apartheid or the effectiveness / appropriateness of the anti-apartheid movement. Newmatilda.com - Comments
  • Whereas hyperbolic activity and elliptic motion characterizes the cab, a big rig manifests an elliptic activity and hyperbolic motion.
  • All accompanied by some dodgy spelling and hyperbolic punctuation. Times, Sunday Times
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  • Debates help them break through the blaze of hyperbolic attacks and confusing countercharges.
  • Any object with a parabolic or hyperbolic trajectory moves so fast that it will never return.
  • Þ sech x ¼ 2 = ðex þ eÀx Þ coth x ¼ ðex þ eÀx Þ = ðex À eÀx Þ Now let's look at the graphs of the six hyperbolic functions. Recently Uploaded Slideshows
  • But it was the subsequent item on hyperbolic crochet that charred the fishcakes beyond redemption. Times, Sunday Times
  • According to the data statistics of max transformation aside of pit to time, the paper established 3 typical hyperbolic function of displacement to time (depth).
  • They were harridans, engaged in a harangue of hermeneutics, harpooning his hyperbolic sense of hagiocracy, calling him a haggard hooligan hamming up a heedless hegemonic hullabaloo. Martin Marks: Bushenschadenfreude: Where has it all Gone?
  • But in neither of those propositions does one find the "I" which, for Descartes, was the necessary bastion against hyperbolical doubt.
  • In this net, the input and output layers are linear, and the hidden layer has neurons with a hyperbolic tangent transfer function.
  • CHAPTER 4 Hyperbolic Functions 65 arcsinh x ¼ ln ½x þ ðx2 þ 1Þ1 = 2 Š arccosh x ¼ ln ½x þ ðx2 À 1Þ1 = 2 Š arctanh x ¼ 0: 5 ln ½ð1 þ xÞ = ð1 À xÞŠ arccsch x ¼ ln ½xÀ1 þ ðxÀ2 þ 1Þ1 = 2 Š arcsech x ¼ ln ½xÀ1 þ ðxÀ2 À 1Þ1 = 2 Š arccoth x ¼ 0: 5 ln ½ðx þ 1Þ = ðx À 1ÞŠ In these expressions, the values 0.5 represent exactly 1 = 2. Recently Uploaded Slideshows
  • He studied time dependent hyperbolic partial differential equations and also began to work on the Cauchy problem.
  • In other words, in the hyperbolic disc the rectangles needed for the argument simply do not exist.
  • It is an open question, however, when such declarations are to be taken as identity assertions, with pantheistic or acosmic intentions, and when they are perhaps hyperbolic variations on descriptions of union-type experiences. Mysticism
  • Talmudists speak much, and hyperbolically enough: which nevertheless they confess to be turned long since into miserable barrenness; but are dim-sighted as to the true cause of it. From the Talmud and Hebraica
  • THE OTHER FOUR The remaining four hyperbolic functions follow from the hyperbolic sine and the hyperbolic cosine, like this: tanh x ¼ sinh x = cosh x csch x ¼ 1 = sinh x sech x ¼ 1 = cosh x coth x ¼ cosh x = sinh x In terms of exponential functions, they are expressed this way: tanh x ¼ ðex À eÀx Þ = ðex þ eÀx Þ csch x ¼ 2 = ðex À eÀx Recently Uploaded Slideshows
  • We can go ahead and bend the octagon into three dimensions to get an idea of the topology generated by this tiling of the hyperbolic plane.
  • The hyperbolic dodecahedron is quite symmetric and has the same symmetry group as a regular dodecahedron. Wolfram Blog : Making the Mathematica 6 Spikey
  • Other examples will be given later in the paper when we discuss packings in hyperbolic spaces.
  • HYPERBOLIC ARCSECANT Figure 4-11 is a graph of the function y ¼ arcsech x (or y ¼ sechÀ1 x). Recently Uploaded Slideshows
  • a hyperbolic style
  • I know that I have exaggerated or made hyperbolic the abuse in my family when talking about it tangentially, either out of black humor or bitterness.
  • For two bodies, the solution is easy: the two bodies move around each other in elliptical orbits - or follow parabolic or hyperbolic paths in some special cases.
  • I think I see you -- for I try to see you in the flesh as I write these sentences -- I think I see you leap at the word pigsty, a hyperbolical expression at the best. Father Damien, an Open Letter to the Reverend Dr. Hyde of Honolulu
  • It's all smoke 'n mirrors lad, you hyperbolic cholic alcoholic she giggled. She tolled me
  • As is usually the case with Washington windbags, these claims are hyperbolic.
  • The saddle-shaped structure is also known as a hyperbolic paraboloid surface, or an anticlastic surface. Sheila Patek clocks the fastest animals
  • The sine function, hyperbolic tangent, and other non-linear variations on these basic ideas have also been used.
  • Quincey's hyperbolical description of the English mail-coach, one cannot down the desire to place that remarkable man on the pilot of the White The Shrinkage of the Planet
  • A relative newcomer named Hakaan Yildirim, who won Paris's prestigious Andam award for young talent, was a victim of boastful handlers who described him in hyperbolic terms he could never live up to. Zac Posen, Hakaan Yildirim among designers outshone in the City of Light
  • A near hyperbolic relationship between respiration rates and meristem radii was observed.
  • So let's take a less hyperbolic look at the English on a night out. Times, Sunday Times
  • We have already looked at this one above, but here we note that, using hyperbolic trig. functions, it is also cosh / sinh or 1 / tanh.
  • Avoid hyperbolic language and narration that pump air into stories that have no real substance.
  • Today we call these three geometries Euclidean, hyperbolic, and absolute.
  • The sinh, cosh, and tanh subroutines compute the hyperbolic trigonometric functions of their parameters.
  • Once again, the speaker took a moment to state that he felt this method would eventually become feasible, once the problems of hyperbolic re-entry and high-energy propellant use in return stages were faced.
  • Karl Gauss pioneered hyperbolic geometry
  • He will support his arguments with many stories of the wonderful instinct and percipiency displayed by his animals; all of which stories, though exceedingly marvellous, obtain implicit credence in the mind of the narrator; and only come short, in point of hyperbolical marvel, of the wonderful utterance of Tom Connor's cat, in the plain Anglo-Saxon vernacular. Fern Vale (Volume 1) or the Queensland Squatter
  • When Russians talk of their politicians, they frequently speak of "thieves," "bandits," and "swindlers" — and not hyperbolically: the presence of criminals in the Duma is a well-publicized fact. Russia Is Finished
  • We can go ahead and bend the octagon into three dimensions to get an idea of the topology generated by this tiling of the hyperbolic plane.
  • When I say "cartoonishly," I mean probably a solid third of the words of this novel are devoted to telling just how mean the Nightside's streets are, in terms so escalatingly hyperbolic the effect really becomes humorous--intentionally, I hope. Archive 2009-04-26
  • It didn't stop there: other celestial objects, such as certain comets, were found to move along hyperbolic orbits.
  • These hyperbolic claims are, of course, part of normal election rhetoric. Times, Sunday Times
  • This model consists the hyperbolic partial differential equations, boundary conditions and cyclical conditions of the system.
  • Figure 33 shows a tessellation of the hyperbolic disc by regular pentagons.
  • And that someone who agrees with you (generally) can still think your post is hyperbolical, mean-spirited, and (perhaps most damning of all) not funny? The Volokh Conspiracy » Rehabilitating Pharaoh
  • Results show that it's rational to illustrate the relationship between skin friction and relative displacement by hyperbolic function.
  • The shortlist is completed by The Changing World of Inflammatory Bowel Disease and Crocheting Adventures with Hyperbolic Planes, which informs its readers how to "crochet models of the hyperbolic plane, pseudosphere, and catenoid/helicoids", as well as exploring geometry and its historical connections with art, architecture, navigation and motion, and the history of crochet. Culture | guardian.co.uk
  • But it was the subsequent item on hyperbolic crochet that charred the fishcakes beyond redemption. Times, Sunday Times
  • Sorry if that sounds a tad hyperbolic. Times, Sunday Times
  • Here again, this rhetoric is inflated, hyperbolic and unjustified.
  • Where "dictatorship" becomes somewhat less hyperbolic is with regard to the policy-based presidential veto that I have previously railed against. Balkinization
  • Once she got the hang of it, she realised that you can see just how parallel lines behave on the hyperbolic plane. Times, Sunday Times
  • For example, Sir William's hyperbolic language lends itself to hyperbolic gestures that contribute to the comic business of his scenes.
  • Sorry if that sounds a tad hyperbolic. Times, Sunday Times
  • In fact, it corresponds to the graph of a function called the hyperbolic cosine.
  • Ah, well, we just may have "outsmarted" ourselves, perhaps as a result of creation of the technologies we are now so dependent on and have begun to realize, belatedly, have also outstripped our ability to regulate within the population increase's hyperbolic upward curve and in co-evolutionary harmony with the finite resources and resiliancy of our planet's biosphere. Posthuman Blues
  • Many people are familiar with Escher's endless staircases, hyperbolic tilings, Möbius ants, intricate tessellations, and other creations.
  • It's much easier to be hyperbolic, or dismissive, or to give up trying to make judgments and just stick to writing lists.
  • Clearly the megalosaurus in the opening passage of Bleak House is a flight of hyperbolic fancy (inspired, I would guess, by the papier-mâché dinosaurs constructed for the Crystal Palace Exhibition, a couple of years earlier).
  • Escher came across an article written by Coxeter, and again whilst unable to understand the text, he was able to determine the rules regarding hyperbolic tessellations using only the diagrams in the paper.
  • Is it excessively hyperbolic to call them worthless scum?
  • These hyperbolic claims are, of course, part of normal election rhetoric. Times, Sunday Times
  • Whereas hyperbolic activity and elliptic motion characterizes the cab, a big rig manifests an elliptic activity and hyperbolic motion.
  • Where are they now, these gold medallists from less hyperbolic days? Times, Sunday Times
  • See this issue's mystery mix for a comparison of Euclidean, hyperbolic, and spherical geometry.
  • I'd write effusively about how we need more politicians like Mr. Bennet – people with serious decisions to make who are willing and able to ignore the constant hyperbolic crap that passes as 'citizen journalism' and 'new media'. Freshman Dem: Passing health care reform worth losing my seat
  • In Alroy’s hyperbolic self-dramatisation is the thinly disguised voice of the young frustrated Disraeli who has not yet begun to fulfil the ‘ideal ambition’ of which he wrote in his diary. Schwarz 1 - Criticism - Critical Contexts
  • Once she got the hang of it, she realised that you can see just how parallel lines behave on the hyperbolic plane. Times, Sunday Times
  • Among closed surfaces, spherical, flat, and hyperbolic geometry are mutually exclusive.
  • The phrase most news agencies use when describing a big storm is that it "paralyzes" an area, and for once it's not that hyperbolic. HolyCoast.com
  • Although this language sounds hyperbolic, it was by no means atypical of audience responses.
  • I mean I liked it as much as I like finding the centres, vertices, foci, and asymptotes of various hyperbolic graphs.
  • You'd think -- from the chorus of hysterical, hyperbolic sky-is-falling reactions of Chicago's gabbiest aldermen -- that Ferguson was recommending bank robbery and drug dealing to balance the budget, and endorsing Al Capone for mayor. Andy Shaw: City Council Says Boo, But We Think Chicago IG's Budget Is a Treat
  • These two pairs of hyperbolic curves can be used for graphical analysis of these two different processes.
  • Her portrait of her runaway ex-husband Tadeusz is equally hyperbolical.
  • Bloom knows how over the top all this is: “I do not fear being called hyperbolical, since the Critical Sublime is precisely that.” Sacred Texts
  • These soon became known as Barlow's Tables and this work gives factors, squares, cubes, square roots, reciprocals and hyperbolic logarithms of all numbers from 1 to 10 000.
  • All those of whom we read such [197] hyperbolical eulogiums, as of Anatomy of Melancholy
  • He fluctuates ambiguously between sexual identities: On the one hand, he is hyperbolically heterosexual, with a voracious appetite for women; on the other hand, he is effete and always primped.
  • Meaningful state complement is further classified into ordinary meaningful state complement, hyperbolical meaningful state complement and degree meaningful state complement.
  • Read together with my matter-of-fact statements, Liszt's hyperbolical and circumlocutional poetic prose will not be misunderstood by the reader. Frederic Chopin as a Man and Musician
  • They are known as the hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cosecant, hyperbolic secant, and hyperbolic cotangent. Recently Uploaded Slideshows
  • Where are they now, these gold medallists from less hyperbolic days? Times, Sunday Times
  • So when notoriously purist and discerning jazz critics single out a rising star to heap hyperbolic praise upon, gig after gig, it really is time to sit up and take notice.
  • A recent Global Research article by Tom Burghardt provides a chilling (if also somewhat hyperbolic) account of recent raids on activists in what many are now calling a reprise on the 1960s CONTELPRO project, which was aimed mainly at the Black Panthers and other black militant groups. Michael Schwartz: Unfortunately, Obama Is Expanding the Imperial Presidency
  • But once again — and take it from someone who generally agrees with you — your satire comes across as petty, hyperbolical, and mean. The Volokh Conspiracy » Rehabilitating Pharaoh
  • The poem opens hyperbolically with an image of an innocent young nymph who spends her days reclining in the grass.
  • Orlando communicates with Shel in a secret language of hyperbolic expressive power.
  • The hyperboloid is then indented and connected to a series of hyperbolic paraboloids through their common directrices, thereby leading the ensemble toward the four load-bearing points to the ground.
  • The assets - too many to list - are being drowned in the hyperbolic ink that is spilled by the naysayers and the do-nothings.
  • I think I see you — for I try to see you in the flesh as I write these sentences — I think I see you leap at the word pigsty, a hyperbolical expression at the best. Lay Morals
  • Even if one goes so far as to say that the use of flashlight powder is ‘dangerous’, it is hyperbolical to describe it as ‘extra-hazardous’.
  • The worst of these titles inflate their claims to hyperbolic levels. The Full Feed from HuffingtonPost.com
  • Where are they now, these gold medallists from less hyperbolic days? Times, Sunday Times
  • The sinh, cosh, and tanh subroutines compute the hyperbolic trigonometric functions of their parameters.
  • I mean, in the media, all the time, the thing that we're most interested in is the most sensational, the most hyperbolic.
  • According to the publisher's hyperbolical publicity, the book covers ‘every aspect’ of Western medical history.
  • A hyperbolic citation reiterates a normative notion in an exaggerated way in order to simultaneously work against it.
  • Here the play took off, and the exaggeration of the suits, which their hyperbolic language, seemed apt to text and production.
  • As Paul studies for his Series 7 exam, Kimberly massages the gums of a basenji, and a former tech writer whips something other than hyperbolic verbiage into submission, I find myself feeling strangely hopeful.
  • That hyperbolical “old rule” should be approached with a huge grain of salt. Unhappy historic anniversary yesterday: the Enabling Act of 1933
  • I am not being even slightly hyperbolical or indulging in tongue in cheek rhetoric when asserting that the Democrats must pray for a national disaster. Come Back July 20, Arnold Kling | EconLog | Library of Economics and Liberty
  • But it was the subsequent item on hyperbolic crochet that charred the fishcakes beyond redemption. Times, Sunday Times
  • SOLUTION 4-1 Remember that the hyperbolic cosecant (csch) is the reciprocal of the hyper - bolic sine (sinh). Recently Uploaded Slideshows
  • There is therefore no marked distortion of the isoseismal lines when crossing the hyperbolic band, while the isacoustic lines are completely diverted from their normal course. A Study of Recent Earthquakes
  • Based on CORDIC algorithm, research reveals how to calculate hyperbolic function by simple hardware.
  • You'd think--from the chorus of hysterical, hyperbolic sky-is-falling reactions of Chicago's gabbiest aldermen--that Ferguson was recommending bank robbery and drug dealing to balance the budget, and endorsing Al Capone for mayor. Andy Shaw: City Council Says Boo, But We Think Chicago IG's Budget Is a Treat
  • He praises her perfection in hyperbolic, mythological terms in the long speech which precedes the choric conclusion to the play.
  • This last result, known by his name, expressed a hyperbolic arc in terms of two elliptic ones.
  • Many people are familiar with Escher's endless staircases, hyperbolic tilings, Möbius ants, intricate tessellations, and other creations.
  • If it means that I grow a little too fervid, or perhaps even hyperbolical, in extolling my native land, I admit the full justice of the remark. Nicholas Nickleby
  • Here we note that, using hyperbolic trig. functions, it is also cosh/sinh or 1/tanh.
  • Husain Haqqani, Pakistan's ambassador to Washington, has dismissed such warnings as hyperbolic and accused US officials and analysts of being guilty of a "panic reaction".
  • • This coherent emission of bioluminescence (having the characteristics of a \ "bio-laser\" emission) was demonstrated by using high technology and methodology, such as a photomultiplier, that is able to determine the Poissonian Photocount Statistics of a \ "biophoton emission\" and the hyperbolic-like relaxation of \ "delayed luminescence\" by analyzing the \ "biophoton emission\" and the Recently Uploaded Slideshows
  • If that sounds hyperbolic, it's worth imagining how you would feel with your name on your chest all day. Times, Sunday Times
  • In fact, it corresponds to the graph of a function called the hyperbolic cosine.
  • All accompanied by some dodgy spelling and hyperbolic punctuation. Times, Sunday Times
  • It has become more vindictive and hyperbolic by the day, with much of the personal venom being directed at him. Times, Sunday Times
  • He found the standard addition formulas for hyperbolic functions, their derivatives and their relation to the exponential function.
  • The arc pressure distribution is in concordance with the hyperbolical curve and the current density distribution is in concordance with the Guass distribution under the presented experiment condition.
  • For the rest of us, the next four years cannot be spent at this pitch of hysteria, indulging in hyperbolic predictions about the end of civilisation. Times, Sunday Times
  • I mean, in the media, all the time, the thing that we're most interested in is the most sensational, the most hyperbolic.
  • They should answer hyperbolic attacks with exaggerated speech of their own, if that's what it takes to stave off political annihilation.
  • In accordance with another embodiment of the present invention, the head assembly includes an hyperbolic reflector.
  • But In regards to our dialog and you attaching arguments to me that I did not make while engaging in hyperbolic statements addressed to me, I can. Sex and the single Marvel super heroine | Robot 6 @ Comic Book Resources – Covering Comic Book News and Entertainment
  • Not really the old days, but their hyperbolic memory updated and brought to life by the power of new dreams. THE MANANA MAN
  • This is a representation of a pentagonal tiling of the hyperbolic plane in which four pentagons meet at each vertex.
  • Earlier this year a legendary figure in the hyperbolical world of ‘supermarket’ tabloids, the inimitable Eddie Clontz, died.
  • I will be singing her praises with hyperbolic terms of exaltation, extolling her to the highest degree, her aura will be raised to mythical proportions.
  • But these hyperbolic hosannas are, unfortunately, no substitute for a rebirth of modern political leadership, which, in fact, continues to wither on the vine.
  • Moreover, the geometries axiomatized in the book have consistent and decidable extensions, namely, Euclidean or hyperbolic geometry over real-closed fields.
  • Around this time Menger's interests in mathematics broadened and he began to work on hyperbolic geometry, probabilistic geometry and the algebra of functions.
  • Schauder's fixed point theorem and his skillful use of function space techniques to analyse elliptic and hyperbolic partial differential equations are contributions of lasting quality.
  • Real tragedies do not need hyperbole, for they are intrinsically hyperbolic.
  • Part of what makes his doubts hyperbolic is that their extravagance renders them unlikely to dislodge our existing beliefs.
  • These are known as the hyperbolic arcsine, hyperbolic arccosine, hyperbolic arctangent, hyper - bolic arccosecant, hyperbolic arcsecant, and hyperbolic arccotangent. Recently Uploaded Slideshows
  • Her efforts combined tools as diverse as hyperbolic geometry, classical methods of automorphic forms and symplectic reduction to obtain results on three different mathematical questions. Princeton University Top Stories
  • You engaged in hyperbolic vitriol and attempted to turn my stance into one of a patronizing controlling male incapable of comprehending your world view. Sex and the single Marvel super heroine | Robot 6 @ Comic Book Resources – Covering Comic Book News and Entertainment
  • Identify the quadric surface given by z. 4 16 (a) Elliptic cone (b) Elliptic paraboloid (c) Hyperbolic paraboloid Recently Uploaded Slideshows
  • Recently, inspired by an article on artistic representations of the hyperbolic plane, McIntyre tried a slightly different approach.
  • In an extravagant, hyperbolic and amusing oration, he asked the question: ‘Why write?’
  • Ron claims that a story Ronald Reagan told about being "clobbered" by his father was hyperbolic - "Hitting kids, I'm happy to report, simply doesn't seem to be in the Reagans' DNA," Ron writes. The uneasy namesake
  • Her efforts combined tools as diverse as hyperbolic geometry, classical methods of automorphic forms and symplectic reduction to obtain results on three different mathematical questions. Princeton University Top Stories
  • hyperbolic functions
  • A large part of the difficulty is that the discourse of the populist Right is also often characterised by irrationalism and hyperbolic abuse.
  • Finally, we construct 3 D highly directive antenna based on the hyperbolic medium.
  • As soon as the kettle boiled, I made porridge and coffee; and that, beyond the literal drawing of water, and the preparation of kindling, which it would be hyperbolical to call the hewing of wood, ended my domestic duties for the day. The Silverado Squatters
  • Amazingly enough, the tone of the article is a throwback to the hyperbolic language of the boom.
  • CHAPTER 4 Hyperbolic Functions 65 arcsinh x ¼ ln ½x þ ðx2 þ 1Þ1 = 2 Š arccosh x ¼ ln ½x þ ðx2 À 1Þ1 = 2 Š arctanh x ¼ 0: 5 ln ½ð1 þ xÞ = ð1 À xÞŠ arccsch x ¼ ln ½xÀ1 þ ðxÀ2 þ 1Þ1 = 2 Š arcsech x ¼ ln ½xÀ1 þ ðxÀ2 À 1Þ1 = 2 Š arccoth x ¼ 0: 5 ln ½ðx þ 1Þ = ðx À 1ÞŠ In these expressions, the values 0.5 represent exactly 1 = 2. Recently Uploaded Slideshows
  • A frustrated thespian, he enjoyed delivering long-winded, hyperbolic, and melodramatic speeches that rolled off his tongue in a rich bass voice.
  • Kurosawa's, by contrast, exaggerate the theme, casting it in the hyperbolic terms of a dread-inducing and sometimes even apocalyptic horror.
  • Egregium specimen dent, saith Erasmus, let them approve themselves worthy first, sufficiently qualified for learning and manners, before they presume or impudently intrude and put themselves on great men as too many do, with such base flattery, parasitical colloguing, such hyperbolical elogies they do usually insinuate that it is a shame to hear and see. Anatomy of Melancholy
  • Oct. 16: "Hyperbolic Crochet Coral Reef" A recent discovery of geometry in coral reefs is looked at through crochet to honor an ecosystem harmed by pollution and climate change. A sampling from area museum exhibits
  • I discussed ‘Symbolism’ with Winthrop as we lunched on stale potato chips and water, but Winthrop was in no mood for hyperbolic gab.
  • But it was the subsequent item on hyperbolic crochet that charred the fishcakes beyond redemption. Times, Sunday Times
  • In freeing women from corsets and dissolving the fortified grandeur of the obdurate, hyperbolic silhouette, Poiret effected a concomitant revolution in dressmaking, one that shifted the emphasis away from the skills of tailoring to … the skills of draping. The King Is Dead
  • We shall look at the asymptotics of the barycentres of independent copies of Brownian motions on the hyperbolic spaces.
  • The "Hyperbolic Crochet Coral Reef" is, amazingly, just what it sounds like: an enormous crocheted coral reef created by hundreds of local crafters, a spinoff from the worldwide Hyperbolic Crochet Coral Reef Project. NASA's 'Extreme Planet Makeover'; Crochet Coral Reef at the Smithsonian
  • If that sounds hyperbolic, it's worth imagining how you would feel with your name on your chest all day. Times, Sunday Times
  • So let's take a less hyperbolic look at the English on a night out. Times, Sunday Times
  • The following formula holds for all real numbers x except 0: coth À x ¼ Àcoth x HYPERBOLIC SINE OF DOUBLE VALUE The hyperbolic sine of twice any given variable is equal to twice the hyper - bolic sine of the original variable times the hyperbolic cosine of the original variable. Recently Uploaded Slideshows

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