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Topic: Trigonometric identity

Related Topics

Trigonometric function

Table of integrals

Cosecant

List of integrals of trigonometric functions

Squeeze theorem

Trigonometric function

Arcsine

Inverse function

Trigonometric substitution

Pythagorean trigonometric identity

Cosine

Golden function

Eulers formula in complex analysis

List of trigonometry topics

	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.
		These identities are useful whenever expressions involving trigonometric functions need to be simplified.
		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.
	en.wikipedia.org /wiki/Trigonometric_identity (1318 words)

	Trigonometric function (Site not responding. Last check: 2007-11-07)
		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)).
	hallencyclopedia.com /Trigonometric_function (3059 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)

	Trigonometric identity (Site not responding. Last check: 2007-11-07)
		In mathematics, trigonometric identities are equalities involving trigonometric functions that are true for all values of the occurring variables.
		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.
		If the trigonometric functions are defined in terms of geometry, then their derivatives can be found by first verifying two limits.
	www.sciencedaily.com /encyclopedia/trigonometric_identity (1158 words)

	The Shortest Path To Trigonometric Identities
		In contrast, asking for a proof of the identity sin(x)+sin(y) = 2sin((x+y)/2)cos((x-y)/2) is analagous to asking for a proof of the identity 2258745004684033 = (27439297)(82317889) A proof (or disproof) of a given proposition is generally easier than constructing the proposition in the first place.
		A similar approach was used to construct the tables of standard trigonometric identities.
		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)

	SparkNotes: Trigonometric Identities: Trigonometric Identities
		Now that we know the definitions of the trigonometric functions, and have a clear understanding how they behave as an angle changes, we can explore the relationships that exist between them.
		A trigonometric identity is an equation involving trigonometric functions that can be solved by any angle.
		We'll take a look at the eight fundamental trigonometric identities, and then some additional identities concerning negative angles (angles in which the rotation between the initial and terminal side is clockwise).
	www.sparknotes.com /math/trigonometry/trigonometricidentities/summary.html (198 words)

	Hyperbolic function - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		The parameter t is not a circular angle, but rather a hyperbolic angle which represents twice the area between the x-axis, the hyperbola and the straight line which links the origin with the point (cosh t, sinh t) on the hyperbola.
		The hyperbolic functions satisfy many identities, all of them similar in form to the trigonometric identities.
	xahlee.org /_p/wiki/Sinh.html (305 words)

	Trigonometric function - (Site not responding. Last check: 2007-11-07)
		In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena.
		Equivalent to the right-triangle definitions, the trigonometric functions can be defined in terms of the rise, run, and slope of a line segment relative to some horizontal line.
		Such tables have been available for as long as trigonometric functions have been described (see History, above), and were typically generated by repeated application of the half-angle and angle-addition identities starting from a known value (such as sin(π/2)=1).
	psychcentral.com /psypsych/Cosine (3984 words)

	[No title]
		NOTE: Unless stated otherwise, assume the domain of each variable in a trigonometric expression is the set of all real numbers or angles for which the expression is meaningful.
		Alternative Technique: Another method of verifying a trigonometric identity involves transforming the left side into an intermediate expression and, transforming the right side into the same intermediate expression; each step in each transformation must be reversible.
		Technique: The technique of trigonometric substitution is a method of changing the form of an algebraic expression into a trigonometric expression.
	www.math.iupui.edu /~vvf/lecturenotes/lecture7_1.doc (340 words)

	CliffsNotes::Trigonometry Glossary (Site not responding. Last check: 2007-11-07)
		identities for negatives: fundamental identities that involve the basic trig functions of negative angles.
		identity: an equation made up of trigonometric functions of an angle that is valid for all values of the angle Also called trigonometric identity.
		Pythagorean identities: fundamental identities that relate the sine and cosine functions and the Pythagorean Theorem.
	www.cliffsnotes.com /WileyCDA/Section/id-106382.html (616 words)

	Pythagorean trigonometric identity - Wikipedia, the free encyclopedia
		Please also consider changing this notice to be more specific.
		The Pythagorean trigonometric identities say that for any number x,
		In case x is an angle between 0 and a right angle, one may use the identities
	en.wikipedia.org /wiki/Pythagorean_trigonometric_identity (100 words)

	M-1000 Review of mistakes
		In all other cases the "identities" (*) are a mistake.
		The only question where a trigonometric identity played a decisive role was #9a.
		Another question where a similar identity could be recalled to simplify the answer was #5c.
	www.cs.mun.ca /~sergey/Winter03/m1000/Final/mistakes.html (807 words)

	Fundamental Trigonometry Identities
		The purpose of verifying an identity is to prove that the two sides of the equation are equal.
		There is never going to be an identity with more than three differences, at least not that we know of, and it is very important to keep that in mind.
		For conditional identities, you should use all the conditions, and compare the two sides of the goal identity, which you need to prove.
	www.cgtcollege.org /mat193/fund_trig.htm (4418 words)

	Hyperbolic Trigonometric Functions
		trigonometric identity, to obtain the first-order ordinary differential-equation.
		In view of the identity, the foregoing is an identity in E. Hence, the aforementioned pair of equations provide a parametric definition of the ellipse.
		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)

	tan55º.tan65º.tan75º=tan85º (Site not responding. Last check: 2007-11-07)
		This is not an identity, it is an equation.
		A trigonometric identity has variables in it and teh statement is true regardess of the values of the variables.
		We would like to prove an identity that, for a specific value of the variable, gives your equation, but we don't see how.
	mathcentral.uregina.ca /QQ/database/QQ.09.04/jesus1.html (175 words)

	The Six Trigonometric Functions
		The two basic trigonometric functions are: sine (which we have already studied), and cosine.
		The graph, as you might expect, is almost identical to that of the sine function, except for a "phase shift" (see the figure).
		The cosine curve is obtained from the sine curve by shifting it to the left a distance of
	www.zweigmedia.com /ThirdEdSite/trig/trig2.html (898 words)

	Calculus:Further integration techniques - Wikibooks, collection of open-content textbooks
		After integrating by parts, and using trigonometric identities, we've ended up with an expression involving the original integral.
		This transforms a trigonometric integral into a algebraic integral, which may be easier to integrate.
		This method can be used to further simplify trigonometric integrals produced by the changes of variables described earlier.
	en.wikibooks.org /wiki/Calculus:Further_integration_techniques (1594 words)

	Matching Questions (Site not responding. Last check: 2007-11-07)
		Students must examine the overall form of a verification of a trigonometric identity, and they must consider how the different steps are related to one another.
		According to Bloom’s taxonomy paradigm, this is a high level task -- synthesis -- which requires a student to correctly assemble the steps of a proof, by transforming trigonometric expressions to determine the relationship between steps and to recall relevant definitions.
		If students were simply asked to write a proof of the trigonometric identity, they would also have to construct the parts by applying algebraic techniques.
	www.joma.org /images/upload_library/4/vol3/assessment/vidakovic6-mq-ex.html (562 words)

	Trigonometric Form of Ceva's Theorem
		The latter may serve as a source of great many trigonometric identities - some obvious, some much less so.
		Some unexpected identities can be obtained by placing the six points A, B, C at the vertices of a regular polygon.
		We are of course concerned with the case where a regular polygon has three concurrent diagonals.
	www.cut-the-knot.org /triangle/TrigCeva.shtml (394 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		x as is, but we can use a trig identity to simplify this integral.
		But there is identity for the sin (a + b).
		Recall that an improper fraction is a fraction where the degree of the numerator is greater than or equal to the degree of the denominator.
	faculty.eicc.edu /bwood/ma155supplemental/supplemental12.htm (907 words)

	Using the Graphing Calculator with Trig Identities (Site not responding. Last check: 2007-11-07)
		If you need to determine if an equation is a trigonometric identity, you can use your graphing calculator.
		A "formal proof" of a trigonometric identity is done algebraically.
		If the bubble runs over the same graph as the first plotting, the equation is a trig identity.
	mathbits.com /MathBits/TISection/trig/trigidentity.htm (94 words)

	General (non-symmetric) triangle wave
		The most general way of dealing with linear combinations of elementary (parabolic and/or sawtooth) waves is to go back to the Fourier components, as we did in finding the series for the elementary waves themselves.
		But in this particular case we can use a trigonometric identity to avoid the extra work of converting back and forth.
		Applying the identity to all the terms of the expansion for
	www-crca.ucsd.edu /~msp/techniques/latest/book-html/node181.html (352 words)

	Trigonometric Identity (Site not responding. Last check: 2007-11-07)
		AoPS Math Forum :: View topic - Trigonometric Identities......
		The Use of Tridiagonal Matrices in Generating Trigonometric Identities...
		Trigonometric identity -- Facts, Info, and Encyclopedia article...
	www.scienceoxygen.com /math/84.html (111 words)

	Trigonometric Identities Lesson (Site not responding. Last check: 2007-11-07)
		Trigonometric identities have less to do with evaluating functions at specific angles than they have to do with relationships between functions.
		Each of these three main identities have two variations on them.
		NOTE #1: The first step to easy solving is to change all possible terms to a form sin and/or cos.
	sacademy.cbv.ns.ca /grsrts/protech11/trigidentities.html (216 words)

	[No title]
		PROBLEM 3-3 (a) & (c) (a) EMBED Equation.3 There is a trigonometric identity that states: EMBED Equation.3 .
		(c) EMBED Equation.3 Using the same trigonometric identity of part (a), we have: EMBED Equation.3 There is another trigonometric identity which states that: EMBED Equation.3 .
		Then: EMBED Equation.3 (c) For the even square wave: EMBED Equation.3 Due that the signal is even: EMBED Equation.3 The last equality was obtained after applying the same identity for the sin of the sum of two angles that was used in problem 3-4.
	www.egr.uh.edu /courses/ece/ECE3337/_private/H3sol.doc (926 words)

	Complex Analysis
		Additionally, it is easy to show that cos(z) and sin(z) are entire functions.
		With these definitions in place, it is now easy to create the other complex trigonometric functions, provided the denominators in the following expressions do not equal zero.
		Since the series for the complex sine and cosine agree with the real sine and cosine when z is real, the remaining complex trigonometric functions likewise agree with their real counterparts.
	math.fullerton.edu /mathews/c2002/ca0504.html (326 words)

	Electron Blue
		I feel, pedantic and dull as it sounds, that I must go through all of these identities and learn them and learn how to work with them, lest I be caught short in the middle of some calculation somewhere way in the future.
		The identity problems are teaching me a way to look at mathematics which I could describe either as the "Russian nesting doll" model, or the "Chinese box" model, or perhaps the "Japanese Transformer Robot" model.
		And then that new entity was itself part of yet another trigonometric statement which could be re-stated to match its neighbors, thus working another transformation which eventually unfolded or infolded into the desired configuration.
	www.pyracantha.com /cgi-bin/blosxom.cgi/2004/03/29 (620 words)

	Inverse Trigonometric Functions
		You probably remember from high school that there are many occassions in which an angle is specified by giving the value of one of the trigonometric functions at this angle.
		In our usual way, we are able to compute the derivative of the inverse tangent function using implicit differentation.
		This is just another guise for the most famous trigonometric identity:
	www.ugrad.math.ubc.ca /coursedoc/math100/notes/zoo/invtrig.html (297 words)

	Dan Bernstein
		The bibasic trigonometric functions, recently introduced by Foata and Han, give rise to the p,q-tangent numbers and the p,q-secant numbers.
		Under this interpretation, the symmetry of the bibasic trigonometric functions yields a combinatorial identity.
		A combinatorial proof of the identity is desired.
	www.wisdom.weizmann.ac.il /~danber (500 words)

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