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Topic: Trigonometric

	MSN Encarta - Trigonometry
		Two trigonometric angles are equal if they are congruent and if their rotations are in the same direction and of the same magnitude.
		Trigonometric functions are unitless values that vary with the size of an angle.
		The numerical values of the trigonometric functions of any angle can be determined approximately by drawing the angle in standard position with a ruler, compass, and protractor; by measuring x, y, and r; and then by calculating the appropriate ratios.
	encarta.msn.com /encyclopedia_761572350/Trigonometry.html (1306 words)

	Trigonometric identity - Wikipedia, the free encyclopedia
		In mathematics, trigonometric identities are equations involving trigonometric functions that are true for all values of the occurring variables.
		An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
		If the trigonometric functions are defined in terms of geometry, then their derivatives can be found by verifying two limits.
	en.wikipedia.org /wiki/Trigonometric_identity (1281 words)

	Trigonometric function - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-05)
		The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread availability of computers and scientific calculators that provide built-in trigonometric functions for any angle.
		The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin.
		The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 BC), who tabulated the lengths of circle arcs (angle A times radius r) with the lengths of the subtending chords (2r sin(A/2)).
	encyclopedia.worldsearch.com /trigonometric_function.htm (3338 words)

	Encyclopedia: Trigonometric identity
		In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena.
		In various applications of trigonometry, it is useful to rewrite the trigonometric functions (such as sine and cosine) in terms of rational functions of a new variable t.
		Identities Knowledge of nearly nothing beyond trigonometry itself is enough to make clear the nature of some of the applications of trigonometry to such endeavors as navigation, land surveying, building, and the like, but that impression is misleading in that it fails to indicate the nature and enormous variety of the...
	www.nationmaster.com /encyclopedia/Trigonometric-identity (2685 words)

	Generating trigonometric tables (Site not responding. Last check: 2007-11-05)
		Tables of trigonometric function s are useful in a number of areas.
		Interpolation of simple look-up tables of trigonometric functions are still used in computer graphics, where accurate calculations are either not needed, or cannot be made fast enough.
		Another important application of trigonometric tables and generation schemes is for fast Fourier transform (FFT) algorithms, where the same trigonometric function values (called twiddle factors) must be evaluated many times in a given transform, especially in the common case where many transforms of the same size are computed.
	www.serebella.com /encyclopedia/article-Generating_trigonometric_tables.html (858 words)

	Trigonometric functions (Site not responding. Last check: 2007-11-05)
		The use of trigonometric functions arises from the early connection between mathematics and astronomy.
		It is perhaps surprising that the second most important trigonometrical function during the period we have discussed was the versed sine, a function now hardly used at all.
		The hyperbolic trigonometric functions were introduced by Lambert.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Trigonometric_functions.html (1239 words)

	Trigonometric Functions -
		The trigonometric functions of angles are the ratios of the various sides of a triangle...
		Definitions of trigonometric and inverse trigonometric functions and links to their properties, plots, common formulas such as sum and different angles, half and multiple angles, power of functions, and their inter relations.
		If we want to use the trigonometric ratios to define functions of a real number variable, then it is necessary to decide what system of units is to be used to relate angles and numbers.
	functions.faasv.com /index.php?k=trigonometric-functions (699 words)

	Trigonometry?
		Trigonometric functions, often known as the circular functions, are defined in terms of the trigonometric ratios.
		The reduction formulas are trigonometric identities that express the trigonometric ratios of an angle of any size in terms of the trigonometric ratios of an acute angle.
		Trigonometric functions are used in polar coordinates, the system in which the position of a point P is determined by its distance OP from a fixed point O and by the angle that OP makes with an initial line OX (see COORDINATE SYSTEMS, mathematics).
	omega.albany.edu:8008 /mat112dir/trig.html (1095 words)

	Trigono/metriX: the Trigonometric Table and Ancient Reckoning
		With regard to the trigonometric table of ratios, the findings are no different; it would appear as though the ancient cultures may have even chosen some of those historically significant numbers (eg., 189, 288, 1872, 2268, etc.), as of that very table of ratios.
		The trigonometric ratios of a triangle generally are presented as of the sine, cosine, and tangent of a particular angle thereof.
		Firstly, we have shown how the table of trigonometric ratios for the sides and angles of right triangles, which is commonly cited in the literature, may be viewed as of the possible relationships involved in such computations.
	www.earthmatrix.com /trigonometrix/table.htm (2207 words)

	Generating trigonometric tables (Site not responding. Last check: 2007-11-05)
		Tables of trigonometric functions are useful in a number of Before the existence of pocket calculators trigonometric tables were essential for navigation science and engineering.
		Interpolation of simple look-up tables of trigonometric are still used in computer graphics where accurate calculations are either not or cannot be made fast enough.
		Another important application of trigonometric tables and schemes is for fast Fourier transform (FFT) algorithms where the same trigonometric values (called twiddle factors) must be evaluated many times in given transform especially in the common case many transforms of the same size are In this case calling generic library routines time is unacceptably slow.
	www.freeglossary.com /Generating_sinus-tables (707 words)

	Learn more about Trigonometric identity in the online encyclopedia. (Site not responding. Last check: 2007-11-05)
		In mathematics, trigonometric identities are equalities involving trigonometric functions that are true for all values of the occurring variables.
		The last several examples are corollaries of a basic fact about the irreducible cyclotomic polynomials; the cosines are the real parts of the zeroes of those polynomials; the sum of the zeroes is the Möbius function evaluated at (in the very last case above) 21; only half of the zeroes are present above.
		In calculus it is essential that angles that are arguments to trigonometric functions be measured in radians; if they are measured in degrees or any other units, then the relations stated below fail.
	www.onlineencyclopedia.org /t/tr/trigonometric_identity.html (879 words)

	Trigonometric interpolation - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-05)
		In the mathematical subfield of numerical analysis, trigonometric interpolation is a special form of interpolation on the unit circle in the complex plane using trigonometric polynomials.
		Trigonometric functions with differences and rapid and easy method of interpolation
		A formula of trigonometric interpolation: Extract from volume 37 of Rendiconti del circolo matermaticl di Palermo
	encyclopedia.worldsearch.com /trigonometric_interpolation_polynomial.htm (148 words)

	Trigonometric function (Site not responding. Last check: 2007-11-05)
		They may be defined as ratios of two sides of a right triangle containing the angle, or, more generally, as ratios of coordinates of points on the unit circle, or, more generally still, as infinite series.
		Using the theory of Taylor series and the facts that the derivative of sine is cosine and the derivative of cosine is negative sine, one can show that these definitions are equivalent to the ones given above.
		The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 B.C.), who tabulated the lengths of circle arcs (equivalent to an angle A times radius r) with the corresponding chords (equivalent to 2r sin(A/2)).
	www.portaljuice.com /trigonometric_function.html (1684 words)

	Trigonometric function
		The values of the trigonometric functions have been tabulated and can also be computed by calculator.
		These definitions are often used as the starting point in a rigorous treatment of trigonometric functions and their applications (e.g.
		The trigonometric functions are not monotonic, so we must restrict their domains before we are able to define a unique inverse.
	www.fact-index.com /t/tr/trigonometric_function.html (1693 words)

	Derivatives Of Trigonometric Functions -
		Trigonometric functions are useful in our practical lives in diverse areas...
		Table of derivatives for trigonometric functions, i.e., sin, cos, tan, cot, sec, and csc, and inverse trigonometric functions, i.e., arcsin, arccos, arctan, arccot, arcsec, and arccsc.
		several useful trigonometric limits that are necessary for evaluating the derivatives of trigonometric functions.
	functions.faasv.com /index.php?k=derivatives-of-trigonometric-functions (719 words)

	Trigonometric Infinite Series (Site not responding. Last check: 2007-11-05)
		Trigonometric functions can be expanded in power series, which facilitates approximations of the functions in extreme cases.
		One of the most important applications of trigonometric series is for situations involving very small angles.
		For such angles, the trigonmetric functions can be approximated by the first term in their series.
	hyperphysics.phy-astr.gsu.edu /hbase/trgser.html (118 words)

	The Shortest Path To Trigonometric Identities (Site not responding. Last check: 2007-11-05)
		A similar approach was used to construct the tables of standard trigonometric identities.
		The realization that a large class of functions can be represented as power series was one of the most significant turning points in the development of modern mathematics.
		To show how this can be applied to the derivation of trigonometric identities, suppose we want to find an expression for sin(a+b) in terms of the sines and cosines of the individual numbers a and b.
	www.mathpages.com /home/kmath205.htm (657 words)

	Graphing and Trigonometric Functions: Practice Exercises
		Fill-in-the-blanks, putting either sin or cos into the second blank, to create a formula for a trigonometric function, then use our transformational graphing technique to graph it.
		Explain why the amplitude of each of the advanced trigonometric functions (i.e., tan, cot, sec, and csc) is infinite.
		Repeat this Exercise as often as necessary until you are confident in your ability to plot the advanced trigonometric functions.
	campus.northpark.edu /math/PreCalculus/Transcendental/Trigonometric/Graphing/Exercises/exercises.html (308 words)

	Trigonometric Function (Site not responding. Last check: 2007-11-05)
		In mathematics, the trigonometric functions are functionss of an angle, important when studying triangless and modeling periodic phenomena.
		Alternatively, all of the basic trigonometric functions can be defined in terms of a unit circle centered at O (shown above right), and similar such geometric definitions were used historically.
		The image on the right displays a two-dimensional graph based on such a summation of sines and cosines, illustrating the fact that arbitrarily complicated closed curvess can be described by a Fourier series.
	www.wikiverse.org /trigonometric-function (2466 words)

	Trigonometric polynomial (Site not responding. Last check: 2007-11-05)
		In mathematics a trigonometric polynomial is a polynomial
		Any such function a periodic function on the real line with period some multiple of 2π can also be considered as a function the unit circle.
		A basic result is that the trigonometric are dense in the space of continuous functions on the unit circle with the uniform norm.
	www.freeglossary.com /Trigonometric_polynomial (106 words)

	Trigonometric function : Sine
		These definitions are often used as the starting point in a rigorous treatment of analysis since the theory of such infinite series is well known.
		The differentiability and continuity is then easily established, as is Euler's formula relating the trigonometric functions to the exponential function as well as the most remarkable formula in the world.
		The trigonometric functions are not monotonic, so their inverses are not unique.
	www.findword.org /si/sine.html (1415 words)

	KryssTal : Trigonometry
		Values for the Trigonometric Functions for a particular angle can be found in tables or on a calculator as with Logarithms.
		Apart from the three trigonometric functions already defined, there are three more which are their reciprocals.
		When looking at the Trigonometric Functions mathematically, we require a more fundamental unit of angular measure.
	www.krysstal.com /trigonometry.html (1111 words)

	Trigonometric Functions (Site not responding. Last check: 2007-11-05)
		The term "trigonometry" is a combination of the two Greek terms, "trigon" and "metria", which translate as "triangle" and "measurement", and was coined by Bartholomeo Pitiscus in 1595.
		Thus, one might assume that "trigonometric" functions (such as, sin(x), cos(x), tan(x), etc.) would be defined in terms of measurements of triangles.
		While this is the way they are naively defined in most High School textbooks, the earliest known calculations related to these functions were by the Greek mathematician Hipparchus in about 140 BC as measurements of circles (specifically, the lengths of chords of a circle).
	campus.northpark.edu /math/PreCalculus/Transcendental/Trigonometric/index.html (333 words)

	Buecher Kaufempfehlung: Trigonometric Sums in Number Theory and Analysis von Gennady I. Arkhipov bei Gruyter (Site not responding. Last check: 2007-11-05)
		Vinogradov first developed the method of trigonometric sums in the first decades of the twentieth century as a way of solving problems in analytical number theory.
		The authors here present a systematic account of the theory of multiple trigonometric sums, using a unified approach to derive results similar to those of Vinogradov, with the understanding the theory of multiple trigonometric sums has reached the level of completion of one-dimensional sums.
		They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and present purely arithmetic results concerning the solvability of equations in integers.
	www.buchsuche.schnellsuchmaschine.de /3110162660-Trigonometric_Sums_in_Number_Theory_and_Analysis_von_Gennady_I_Arkhipov_bei_Gruyter.html (275 words)

	TRIGONOMETRY FOR STATICS-Part 1
		The trigonometric functions are named sine, cosine, tangent, cotangent, secant, and cosecant.
		The values of the trigonometric functions for this angle are given as:
		The same rule does not apply to negative exponents since the exponent "-1" is reserved for the inverse trigonometric function.
	em-ntserver.unl.edu /Math/mathweb/trigonom/trigsA97.html (264 words)

	Precalculus: Reference/Trigonometry
		The area A of a circular sector determined by a central angle of theta radians in a circle of radius r is given by the following formula.
		There are six trigonometric functions: sine, cosine, tangent, and their reciprocals, cosecant, secant, and cotangent.
		Substitutions and identities are often needed to solve equations involving trigonometric functions.
	www.scit.wlv.ac.uk /university/scit/maths/calculus/modules/topics/precalc/trig/ref.htm (635 words)

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