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Topic: Pythagorean trigonometric identity

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	Trigonometric identity: Definition and Links by Encyclopedian.com
		...Trigonometric identity Trigonometric identity In mathematics, trigonometric...involving trigonometric functions that are true for all values of the occurring...with a trigonometric function, and then simplifying the resulting integral with a trigonometric...
		In mathematics, trigonometric identities are equalities 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.
	www.encyclopedian.com /tr/Trigonometric-Identities.html (984 words)

	Basic Trigonometric Identity (Site not responding. Last check: 2007-11-02)
		Pythagorean trigonometric identity - The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions.
		Along with the sum-of-angles formulae (see trigonometric identity#Angle sum and difference identities) it is the basic relation among the sin and cos functions from which all others may be derived (see trigonometric function#Other definitions for the relevant theorem).
		Trigonometric identity - In mathematics, trigonometric identities are equations involving trigonometric functions that are true for all values of the occurring variables.
	tr74.mtjlcs.com /basictrigonometricidentity.html (955 words)

	Pythagorean trigonometric identity - Wikipedia, the free encyclopedia
		The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions.
		If the trigonometric functions are defined in terms of the unit circle, the proof is immediate: given an angle θ, there is a unique point P on the unit circle centered at the origin in the Euclidean plane at an angle θ from the x-axis, and cos(θ),sin(θ) are respectively the x- and y-coordinates of P.
		The Pythagorean theorem is not closely related to the Pythagorean identity when the trigonometric functions are defined in this way; instead, in combination with the theorem, the identity now shows that these power series parameterize the unit circle, which we used in the previous section.
	en.wikipedia.org /wiki/Pythagorean_trigonometric_identity (750 words)

	Trigonometric function (Site not responding. Last check: 2007-11-02)
		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)).
	www.gogoglo.com /wiki/en/wikipedia/t/tr/trigonometric_function.html (2773 words)

	List of trigonometric identities Summary
		The trigonometric identities are derived by expressing the sine or cosine of a sum of difference of angles in terms of the sines and cosines of the individual angles.
		In mathematics, trigonometric identities are equations involving trigonometric functions that are true for all values of the occurring variables.
		The fact that the differentiation of trigonometric functions (sine and cosine) results in linear combinations of the same two functions is of fundamental importance to many fields of mathematics, including differential equations and fourier transformations.
	www.bookrags.com /List_of_trigonometric_identities (2114 words)

	Pythagorean theorem Summary
		The Pythagoreans formulated a view from an arithmetical standpoint that believed the concept of the number was the key to the qualities of mankind and matter and that it was the ultimate principle of all proportion of the universe.
		The Pythagoreans proved that the square root of two is irrational, and this proof has come down to us even though it flew in the face of their cherished belief that everything was rational.
		Another generalization of the Pythagorean theorem to three dimensions is de Gua's theorem: If a tetrahedron has a right angle corner (a corner like a cube), then the square of the area of the face opposite the right angle corner is the sum of the squares of the areas of the other three faces.
	www.bookrags.com /Pythagorean_theorem (4628 words)

	Proving Trigonometric Identity (Site not responding. Last check: 2007-11-02)
		Identity document - An identity document is a piece of documentation designed to prove the identity of the person carrying it.
		Gagarin between hypotenuse, this tan identity ratio read to as the versed sine (versin = 1 / cos) cosecant (csc = 1 / cos) cosecant (csc = 1 / sin) Several relations between these functions are functionss of an angle is the side opposite to the length of the 1980s.
		Trigonometric function In mathematics, the trigonometric functions are defined in terms of the subject at the present time.
	fi35.mtjlcs.com /provingtrigonometricidentity.html (1664 words)

	Trigonometric identities
		Identities are used for the purpose of giving expressions a more convenient form.
		In calculus and all its applications, the trigonometric identities are of central importance.
		These are called Pythagorean identities, because, as we will see in their proof, they are the trigonometric version of the Pythagorean theorem.
	www.themathpage.com /aTrig/trigonometric-identities.htm (481 words)

	Trigonometric identity
		A geometric proof of the sin(x+y) identity is given at the end of this article.
		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 M bius function evaluated at (in the very last case above) 21; only half of the zeroes are present above.
		Since the circle is an algebraic curve of genus 0, one expects the 'circular functions' to be reducible to rational functions.
	www.black-science.org /wikipedia/t/tr/trigonometric_identity.html (789 words)

	Math 1040 (Site not responding. Last check: 2007-11-02)
		(sin t) that are a composition of the sine, cosine or tangent and the associated inverse trigonometric function where x and t are specific numbers by using the definitions of the inverse trigonometric functions.
		x) that are a composition of the sine, cosine or tangent with an inverse trigonometric function where x is a specific number by using the definitions of the functions involved.
		4.2 - By using the sum and difference identities for the sine and tangent, the double angle identities and the half angle identities, find exact values of the trigonometric functions for angles that can be written as sums, differences, multiples or fractions of angles for which values of the trigonometric functions are known or given.
	www.colorado.edu /math/umap/OneCredit/Objectives/1040.html (436 words)

	Trigonometric Identities : Overall Good (Site not responding. Last check: 2007-11-02)
		Trigonometric Identities - HOME Trigonometric Identities Cliffs Trigonometry by David A. Kay, CliffsQuickReview Trigonometry mirrors the curriculum for a typical trigonometry course, which includes trigonometric functions, trigonometry of triangles, trigonometric identities, vectors, polar coordinates, and complex numbers.
		Trigonometric Function Identity - HOME Trigonometric Function Identity Cliffs Trigonometry by David A. Kay, CliffsQuickReview Trigonometry mirrors the curriculum for a typical trigonometry course, which includes trigonometric functions, trigonometry of triangles, trigonometric identities, vectors, polar coordinates, and complex numbers.
		Trigonometric Identity - HOME Trigonometric Identity Cliffs Trigonometry by David A. Kay, CliffsQuickReview Trigonometry mirrors the curriculum for a typical trigonometry course, which includes trigonometric functions, trigonometry of triangles, trigonometric identities, vectors, polar coordinates, and complex numbers.
	www.mtjlcs.com /134-Trigonometric-Identities.html (2381 words)

	Trigonometric function - ExampleProblems.com
		In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena.
		Trigonometric functions specify the relationships between side lengths and interior angles of a right triangle.
		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.
	www.exampleproblems.com /wiki/index.php/Trigonometric_function (3235 words)

	Identity Hub (Site not responding. Last check: 2007-11-02)
		Identity theft - Identity theft (or identity fraud) is the deliberate assumption of another person's identity, usually to gain access to their finances or frame them for a crime.
		Identity function - In mathematics, an identity function, also called identity map or identity transformation, is a function which does not have any effect: it always returns the same value that was used as its argument.
		Drawing from her own experience identity hub and the recollections of over seventy other granddaughters, Edelman explores the three-generation triangle from which women develop their female identities: the grandmother-mother-daughter relationship.
	www.wire00.com /identityhub.html (693 words)

	TaskStream
		"An equation involving the trigonometric functions which is valid for all values for the angle for which the functions are defined is called a trigonometric identity.
		A trigonometric identity is verified by transforming one member (your choice) into the other.
		Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, con-versely, they can prove the Pythagorean theorem as a consequence of this identity).
	lesson.taskstream.com /lessonbuilder/v.asp?LID=fjz6e7e6elz1hu (1107 words)

	Definition: A trigonometric expression is an expression involving trigonometric functions (Site not responding. Last check: 2007-11-02)
		Technique: To verify a trigonometric identity, we may use the fundamental identities above and algebraic manipulations, and transform the left side (of the given “identity”) into the right side, or vice versa.
		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.htm (202 words)

	Algebra II: Trigonometric Identities - Math for Morons Like Us
		identities are important identities that involve sums or differences of angles.
		An identity that shows that the cosine of the difference of two angles is related to the cosines and sines of the angles themselves.
		These identities are derived using the sum and difference identities.
	library.thinkquest.org /20991/alg2/trigi.html (509 words)

	Mathematics Placement Exam Algebra Review Material s
		An identity is an equation that is true for all values of the variables for which each member of the equation is defined.
		Then, without referring to the statements of the basic identities, fill in the blanks to form one of the reciprocal, quotient or Pythagorean identities, or one of their alternate forms.
		The derivation of this identity involves the distance formula and the Law of Cosines and is somewhat intricate.
	www.math.colostate.edu /dept/IMP/SG/MPE_Review/trigonometry.html (2869 words)

	Reference.com/Encyclopedia/List of trigonometric identities
		If the trigonometric functions are defined in terms of geometry, therefore their derivatives can be found by verifying two limits.
		The integral identities can be found in "list of integrals of trigonometric functions".
		These proofs apply directly only to acute angles, but the truth of these identities in the case of acute angles can be used to infer their truth in more general cases.
	www.reference.com /browse/wiki/Trigonometric_identity (2352 words)

	Trigonometric Functions of Angles in a right triangle (C)
		Trigonometric Functions of Angles in a right triangle (C)
		Recall from the Pythagorean Theorem that a triangle is a right triangle if and only if the sum of the squares on two of its sides equals the square on its third side.
		This identity is sometimes called the Pythagorean Identity, of for reasons that will become clear below, the Circle Identity.
	www.uwm.edu /~ericskey/TANOTES/Trigonometry/node2.html (339 words)

	Algebra II: Trigonometry - Math for Morons Like Us
		The trigonometric ratios are very useful when dealing with triangles and unit circles.
		All six of the trigonometric functions are periodic, that is, their graphs repeat after a certain period.
		The Pythagorean Identities come in handy later on when you need to prove more complicated trig.
	library.thinkquest.org /20991/alg2/trig.html (906 words)

	Pythagorean Theorem : Examples for Trigonometry at the Library of Math (Site not responding. Last check: 2007-11-02)
		In this topic we explain similar triangles and state the Pythagorean Theorem and its converse.
		Succinctly, the Pythagorean Theorem states: in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
		The converse is also true: if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
	www.libraryofmath.com /Trigonometry_Example_Pythagorean_Theorem.html (229 words)

	Sample wording for problems that may be on the test (Site not responding. Last check: 2007-11-02)
		Given the value of one trigonometric function of a number and whether or not another trigonometric function at the same number is positive or negative, determine the value of the trigonometric functions at the number.
		Perform the indicated operations and use trigonometric identities to simplify.
		Evaluate the trigonometric function for the variables indicated making use of the other information given.
	www.georgiasouthern.edu /~jbhawkin/Handouts/MATH1113DHRvwTest3.htm (604 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)

	Finding Values : Examples for Trigonometry at the Library of Math (Site not responding. Last check: 2007-11-02)
		The trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant of an acute angle are defined and detailed with examples and comments.
		The reciprocal properties explain that three of the six trigonometric functions (sine, cosine, and tangent) are just reciprocals of three other trigonometric functions (cosecant, secant, and cotangent).
		Finally, the Pythagorean Identities allows us to find the values of the six trigonometric functions given only one of the values.
	www.libraryofmath.com /Trigonometry_Example_Finding_Values.html (481 words)

	My Space: Trigonometric function (4)
		Among the most frequently used is the Pythagorean identity, which states that for any angle, the square of the sine plus the square of the cosine is always 1.
		The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread availability of
		, where trigonometric series are used to solve a variety of boundary-value problems in partial differential equations.
	jodiemiyo2.spaces.live.com /Blog/cns!AB72C214B92927BF!229.entry (1115 words)

	List of trigonometric identities - Wikipedia, the free encyclopedia
		All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O.
		In some contexts, this notation may serve the pedagogical purpose of emphasizing that one has not yet proved that this is an exponential function.
		and observing that this identity for cis of a sum is simpler than the identities for sin and cos of a sum.
	en.wikipedia.org /wiki/Trigonometric_identity (2010 words)

	Trigonometry
		If the equation contains at least one trigonometric function that is true for some but not all values of the variables then that equation is called to be trigonometric equation.
		If the equation contains a trigonometric function and is true for all the values of the variables then that equation is called to be trigonometric identity.
		Trigonometric Identities includes 3 types, Quotient identities, Reciprocal identities, and Pythagorean identities.
	www.icoachmath.com /SiteMap/Trigonometry.html (179 words)

	Test 3 Concepts
		Important identities: Pythagorean identities (page 225), Sum and difference formulas for the sine and cosine (pages 223/224), Double angle formulas (page 228), Half angle formulas (page 230), Formulas for products of sine and cosine (page 232).
		Pythagorean identities, sum and difference formulas, and double angle formulas will not be given.
		Remember, these functions will only give one value back if you use your calculator, so you will need to use your knowledge of the sine, cosine and tangent graphs to determine the other solutions, if they are applicable.
	math.la.asu.edu /~walker/mat170/conceptstest3.htm (534 words)

	Verifying Trigonometric Identities (Site not responding. Last check: 2007-11-02)
		In calculus it is frequently necessary to rewrite an expression involving trigonometric functions in an equivalent form.
		Recall an identity is an equation that is true for all values of the variable.
		At first verifying trigonometric identities can be difficult and frustrating.
	www.kishwaukeecollege.edu /faculty/ccullop/math155/notes/5.2/5_2.html (615 words)

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