
	Where results make sense

Topic: Hyperbolic sine

Related Topics

8va

In the News (Mon 4 Jun 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Hyperbolic function - Wikipedia, the free encyclopedia
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		The basic hyperbolic functions are the hyperbolic sine sinh, and the hyperbolic cosine cosh, from which are derived the hyperbolic tangent tanh, etc.
		Hyperbolic functions are also useful because they occur in the solutions of some simple linear differential equations, notably that defining the shape of a hanging cable, the catenary.
	en.wikipedia.org /wiki/Hyperbolic_function (498 words)

	Hyperbolic function -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, the hyperbolic functions are analogs of the ordinary (additional info and facts about trigonometric) trigonometric, or circular, functions.
		The hyperbolic functions satisfy many identities, all of them similar in form to the (additional info and facts about trigonometric identities) trigonometric identities.
		The graph of the function cosh x is the (The curve theoretically assumed by a perfectly flexible and inextensible cord of uniform density and cross section hanging freely from two fixed points) catenary curve.
	www.absoluteastronomy.com /encyclopedia/h/hy/hyperbolic_function.htm (407 words)

	CLHS: Function SINH, COSH, TANH, ASINH...
		These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument x as given in the next figure.
		The branch cut for the inverse hyperbolic sine function is in two pieces: one along the positive imaginary axis above i (inclusive), continuous with quadrant I, and one along the negative imaginary axis below -i (inclusive), continuous with quadrant III.
		Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points -i/2 and i/2 excluded.
	www.lisp.org /HyperSpec/Body/fun_sinhcm_co_coshcm_atanh.html (460 words)

	Math 252-Appendix 1
		The hyperbolic sine and cosine functions are defined in terms of exponential functions as follows.
		The other hyperbolic functions tanh(x), sech(x), csch(x), coth(x) are defined as quotients of the hyperbolic sine and cosine in the same pattern as the trigonometric funtions.
		One practical application of the hyperbolic functions (which stems from properties of their derivatives), is to describe the shape of a hanging cable, such as a telephone line between telephone poles.
	oregonstate.edu /instruct/mth252h/Bogley/w02/A1.html (589 words)

	Karl's Calculus Tutor - 11.5 Hyperbolic Substitution
		If hyperbolic substitution is not part of your curriculum, then skip ahead (unless you're curious) to Partial Fractions, and don't worry, we will cover the methods to integrate the functions that are covered here later on.
		Although the derivative of the hyperbolic sine is the hyperbolic cosine, the analogy does not quite stretch to finding the derivative of the hyperbolic cosine.
		The integrands that the hyperbolic functions address are all analogs of the ones that the trig functions were able to address.
	www.karlscalculus.org /hyper.html (2129 words)

	Karl's Calculus Tutor - Derivation of Hyperbolic Sine
		So you know a magic property of this hyperbolic sine function involving its relationship to its own derivative, and from that you want to know the more details about this function.
		Since we are modeling the hyperbolic sine function after the sine function, we would like to make it also an odd function, and these choices for
		the way we do for hyperbolic sine is what strikes our fancy in terms of symmetry and analogy to the sine function.
	www.karlscalculus.org /hyperbox.html (676 words)

	sciforums.com - Relativity and acceleration
		Now me and my lab partner are just required to create a spreadsheet describing the speed and time of transit of a spaceship going to the andromeda galaxy at a constant acceleration of 1g, taking into account the effects of relativity.
		For example, the shape of a hanging chain or rope, such as on a suspension bridge, is described mathematically by the hyperbolic cosine function.
		Hyperbolic functions, fundamentally, are useful in analysing hyperbolas, in the same way that standard trig functions are useful in analysing circles and ellipses.
	www.sciforums.com /printthread.php?t=28733 (228 words)

	Trig/Hyper (Site not responding. Last check: 2007-11-06)
		Trigonometric and hyperbolic functions are different groups of functions, but they are comparable in form and they even use similar names.
		Hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant and hyperbolic cosecant functions.
		Hyperbolic arcsine, hyperbolic arccosine, hyperbolic arctangent, hyperbolic arccotangent, hyperbolic arcsecant and hyperbolic arccosecant functions.
	orefa.com /addup/2/doc/reference/functions/trig (328 words)

	Hyperbolic Trigonometric Functions
		The complex addition theorems for the hyperbolic secent, cosecent, versed sine, and haversed sine are not interesting.
		The McLaurin's series for the hyperbolic sine and cosine may be obtained from their definitions and the series for the exponential function.
		The McLaurin's series formulae for the hyperbolic arc sine, arc cosine, arc cotangent, arc secent, arc cosecent, arc versed sine, arc coverssed sine, and arc haversed sine are not interesting.
	www.geocities.com /ResearchTriangle/2363/hyperbol.html (1630 words)

	ANSI and GNU Common Lisp Document - sinh
		These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument x as given in Figure 12--15.
		The branch cut for the inverse hyperbolic tangent function is in two pieces: one along the negative real axis to the left of -1 (inclusive), continuous with quadrant III, and one along the positive real axis to the right of~1 (inclusive), continuous with quadrant I. The points -1 and~1 are excluded from the domain.
		Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points -\pi i/2 and~\pi i/2 excluded.
	www.mathcs.duq.edu /simon/Gcl/gcl_767.html (523 words)

	ComplexUtils (Math 1.2-dev API) (Site not responding. Last check: 2007-11-06)
		Compute the hyperbolic sine for the given complex argument.
		Compute the hyperbolic cosine for the given complex argument.
		Compute the hyperbolic tangent for the given complex argument.
	jakarta.apache.org /commons/math/apidocs/org/apache/commons/math/complex/ComplexUtils.html (330 words)

	tools.nb
		The arcsine of q equals minus V normalized to V times the hyperbolic arcsine of q times V normalized to V. The arccosine of q equals minus V normalized to V times the hyperbolic arccosine of q.
		The hyperbolic cosine of q equals (hyperbolic cos t cosine absolute value of V, hyperbolic sine t sine of the absolute value of V times V normalized to V)
		The hyperbolic arccosine of q equals the natural log of (q plus or minus the square root of q squared minus one).
	world.std.com /~sweetser/quaternions/intro/tools/s.html (981 words)

	timath.h
		csinh calculates the hyperbolic sine w = sinh(z) of the complex number which real and imaginary parts are z_re and z_im, and stores real and imaginary part of the result in floating point destinations pointed to by w_re and w_im.
		where sinh and cosh are complex hyperbolic sine and complex hyperbolic cosine (see csinh and ccosh).
		It calculates simultaneously the sine, the cosine and the tangent of the floating point value pointed to by xptr, and stores the results in floating point destinations pointed to by sine, cosine and tangent.
	tigcc.ticalc.org /doc/timath.html (7060 words)

	ipedia.com: Hyperbola Article (Site not responding. Last check: 2007-11-06)
		The rectangular hyperbola with the co-ordinate axes as its asymptotes is given by the equation xy=c, where c is a constant.
		Just as the sine and cosine functions give a parametric equation for the ellipse, so the hyperbolic sine and hyperbolic cosine give a parametric equation for the hyperbola.
		A body that has sufficient energy to escape the gravitational field of a massive body moves in a hyperbolic trajectory with the massive body at one of the foci.
	www.ipedia.com /hyperbola.html (388 words)

	Special Functions Documentation
		Hyperbolic functions on r (cosh: purple; sinh: red; tanh: blue)
		The sine Cardinal family of functions is defined by the family of indices
		We define, by analogy, the Hyperbolic sine Cardinal family of functions is defined by the family of indices
	www-eleves-isia.cma.fr /documentation/BoostDoc/boost_1_29_0/libs/math/special_functions/special_functions.html (659 words)

	Hyperbolic Trigonometric Functions
		The MacLaurin's series for the hyperbolic sine and cosine may be obtained from their definitions and the series for the exponential function.
		The MacLaurin's series formulae for the hyperbolic arc sine, arc cosine, arc cotangent, arc secant, arc cosecant, arc versed sine, arc coversed sine, and arc haversed sine are not interesting.
		The values of the inverse hyperbolic trigonometric functions have to be obtained from the foregoing arctangent, by solving the quadratic equations of the identities and
	www.rism.com /Trig/hyperbol.htm (9675 words)

	Inverse Hyperbolic Functions (Site not responding. Last check: 2007-11-06)
		The hyperbolic functions are defined as power series which can be computed (for reals, complex, quaternions and octonions) as:
		The hyperbolic sine is one to one on the set of real numbers, with range the full set of reals, while the hyperbolic tangent is also one to one on the set of real numbers but with range
		The inverse of the hyperbolic sine is called the Argument hyperbolic sine, and can be computed (for
	www.boost.org /libs/math/special_functions/inverse_hyperbolic.html (235 words)

	MB-Cyclopædia for MultiValue Systems
		Sine A = a / c Cosine A = b / c Tangent A = a / b = Sine A / Cosine A
		Hyperbolic tangent A = Tanh A = Sinh A / Cosh A
		Hyperbolic secant = the reciprocal of the hyperbolic cosine Hyperbolic cosecant = the reciprocal of the hyperbolic sine Hyperbolic cotangent = the reciprocal of the hyperbolic tangent
	members.aol.com /mbpublish/mmt57.html (487 words)

	Hyperbolic (JMSL Numerical Library)
		Pure Java implementation of the hyperbolic functions and their inverses.
		Returns the inverse hyperbolic sine of its argument.
		value representing the number whose hyperbolic sine is x.
	www.vni.com /products/imsl/jmsl/v25/api/com/imsl/math/Hyperbolic.html (191 words)

	Search Results for hyperbolic - Encyclopædia Britannica (Site not responding. Last check: 2007-11-06)
		the hyperbolic sine of z (written sinh z); the hyperbolic cosine of z (cosh z); the hyperbolic tangent of z (tanh z); and the hyperbolic cosecant, secant, and cotangent of z.
		The first description of hyperbolic geometry was given in the context of Euclid's postulates, and it was soon proved that all hyperbolic geometries differ only in scale (in the same sense that...
		Perhaps it was this desire for conceptual understanding that made Gauss reluctant to publish the fact that he was led more and more “to doubt the truth of geometry,” as he put it.
	www.britannica.com /search?query=hyperbolic&submit=Find&source=MWTAB (471 words)

	Hyperbolic Functions (Site not responding. Last check: 2007-11-06)
		Description: The asinh function returns the inverse hyperbolic sine of x.
		Description: The sinhcosh function returns both the hyperbolic sine and hyperbolic cosine of x.
		These pages are expected to represent the University of Virginia community and the State of Virginia in a professional manner in accordance with the University of Virginia’s Computing Policies.
	www.itc.virginia.edu /research/intel/docs/c_ug/lm_hypr.htm (152 words)

	GNU Emacs Calc 2.02 Manual - Trigonometric and Hyperbolic Functions (Site not responding. Last check: 2007-11-06)
		Go to the first, previous, next, last section, table of contents.
		If the input is an HMS form, it is interpreted as degrees-minutes-seconds; otherwise, the input is interpreted according to the current angular mode.
		by taking the sine of 45 degrees, regardless of the current angular mode.
	ofb.net /gnu/calc/calc_213.html (356 words)

	Hyperbolic (JMSL Numerical Library)
		Returns the inverse hyperbolic cosine of its argument.
		Returns the inverse hyperbolic tangent of its argument.
		value representing the number whose hyperbolic cosine is x.
	www.vni.com /products/imsl/jmsl/v30/api/com/imsl/math/Hyperbolic.html (191 words)

	[No title]
		Press the appropriate number 1-6 to select the hyperbolic function of choice.
		Press OPTN to view the options menu, press F4 to select HYP and access the hyperbolic functions menu, then press the appropriate number 1-6 to select the hyperbolic function of choice.
		For example, we graph the hyperbolic sine function, sinh.
	www.humboldt.edu /~cmb2/technology/casiofx2indexfiles/hyperbolicfunctions.doc (198 words)

	Hyperbolic functions (Site not responding. Last check: 2007-11-06)
		Trigonometric and hyperbolic functions together with some other functions form a very important class of elementary functions, which are used in mathematics very often.
		Hyperbolic functions are used very widely for modeling of natural phenomena.
		Nikolay Lobatchevski used hyperbolic functions in your non-Euclidean geometry and therefore Lobatchevski's geometry is called hyperbolic geometry.
	www.goldenmuseum.com /0904HyperFunc_engl.html (281 words)

	Function (from lymphatic system) -- Britannica Student Encyclopedia
		Particular functions of the set had been formulated earlier by the Swiss mathematicians Daniel Bernoulli, who studied the oscillations of a chain suspended by one...
		These functions are most conveniently defined in terms of the exponential function, with sinh z = (e e) and cosh z = (e + e) and with the other hyperbolic trigonometric functions defined in a manner...
		Explains the concept of sine with the aid of graphs and examples, and provides access to calculus related resources.
	www.britannica.com /ebi/article-204116 (840 words)

	SCIENTIFIC&MATHEMATICAL CALCULATIONS
		Remarks: Returns the inverse hyperbolic sine of the numeric argument.
		The arc sine is the angle whose sine is equal to the argument.
		Remarks: Returns the hyperbolic sine of the numeric argument.
	www.promsoft.com /dev/oz700sdk/functions.html (752 words)

	Math::Trig - trigonometric functions
		The constant pi is also defined as are a few convenience functions for angle conversions.
		The arcus (also known as the inverse) functions of the sine, cosine, and tangent
		The arcus (also known as the inverse) functions of the hyperbolic sine, cosine, and tangent
	www.perl.com /doc/manual/html/lib/Math/Trig.html (952 words)

Try your search on: Qwika (all wikis)