Data Portal @ linkeddatafragments.org

Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Law_of_cosines> ?p ?o. }

• Law_of_cosines abstract "In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines stateswhere denotes the angle contained between sides of lengths a and b and opposite the side of length c.The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if the angle is a right angle (of measure 90° or π/2 radians), then cos = 0, and thus the law of cosines reduces to the Pythagorean theorem:The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.By changing which sides of the triangle play the roles of a, b, and c in the original formula, one discovers that the following two formulas also state the law of cosines:Though the notion of the cosine was not yet developed in his time, Euclid's Elements, dating back to the 3rd century BC, contains an early geometric theorem almost equivalent to the law of cosines. The case of obtuse triangle and acute triangle (corresponding to the two cases of negative or positive cosine) are treated separately, in Propositions 12 and 13 of Book 2. Trigonometric functions and algebra (in particular negative numbers) being absent in Euclid's time, the statement has a more geometric flavor:Proposition 12In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle.Using notation as in Fig. 2, Euclid's statement can be represented by the formulaThis formula may be transformed into the law of cosines by noting that CH = (CB) cos(π − γ) = −(CB) cos γ. Proposition 13 contains an entirely analogous statement for acute triangles.The theorem was popularized in the Western world by François Viète in the 16th century. At the beginning of the 19th century, modern algebraic notation allowed the law of cosines to be written in its current symbolic form.".
• Law_of_cosines thumbnail Triangle_with_notations_2.svg?width=300.
• Law_of_cosines wikiPageExternalLink cosine.shtml.
• Law_of_cosines wikiPageExternalLink law-of-cosines-formula-examples.php.
• Law_of_cosines wikiPageID "19480890".
• Law_of_cosines wikiPageRevisionID "602126259".
• Law_of_cosines hasPhotoCollection Law_of_cosines.
• Law_of_cosines id "p/c026660".
• Law_of_cosines sign "Euclid's Elements, translation by Thomas L. Heath.".
• Law_of_cosines text "''Proposition 12".
• Law_of_cosines text "In obtuse-angled triangles the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle by twice the rectangle contained by one of the sides about the obtuse angle, namely that on which the perpendicular falls, and the straight line cut off outside by the perpendicular towards the obtuse angle.''".
• Law_of_cosines title "Cosine theorem".
• Law_of_cosines subject Category:Angle.
• Law_of_cosines subject Category:Articles_containing_proofs.
• Law_of_cosines subject Category:Theorems_in_plane_geometry.
• Law_of_cosines subject Category:Triangle_geometry.
• Law_of_cosines subject Category:Trigonometry.
• Law_of_cosines type Abstraction100002137.
• Law_of_cosines type Communication100033020.
• Law_of_cosines type Message106598915.
• Law_of_cosines type Proposition106750804.
• Law_of_cosines type Statement106722453.
• Law_of_cosines type Theorem106752293.
• Law_of_cosines type TheoremsInPlaneGeometry.
• Law_of_cosines comment "In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. Using notation as in Fig.".
• Law_of_cosines label "Cosinusregel".
• Law_of_cosines label "Kosinussatz".
• Law_of_cosines label "Law of cosines".
• Law_of_cosines label "Lei dos cossenos".
• Law_of_cosines label "Loi des cosinus".
• Law_of_cosines label "Teorema del coseno".
• Law_of_cosines label "Teorema del coseno".
• Law_of_cosines label "Twierdzenie cosinusów".
• Law_of_cosines label "Теорема косинусов".
• Law_of_cosines label "قانون جيب التمام".
• Law_of_cosines label "余弦定理".
• Law_of_cosines label "餘弦定理".
• Law_of_cosines sameAs Kosinová_věta.
• Law_of_cosines sameAs Kosinussatz.
• Law_of_cosines sameAs Νόμος_των_συνημιτόνων.
• Law_of_cosines sameAs Teorema_del_coseno.
• Law_of_cosines sameAs Kosinuaren_teorema.
• Law_of_cosines sameAs Loi_des_cosinus.
• Law_of_cosines sameAs Hukum_cosinus.
• Law_of_cosines sameAs Teorema_del_coseno.
• Law_of_cosines sameAs 余弦定理.
• Law_of_cosines sameAs 코사인_법칙.
• Law_of_cosines sameAs Cosinusregel.
• Law_of_cosines sameAs Twierdzenie_cosinusów.
• Law_of_cosines sameAs Lei_dos_cossenos.
• Law_of_cosines sameAs m.0dksp.
• Law_of_cosines sameAs Q164321.
• Law_of_cosines sameAs Q164321.
• Law_of_cosines sameAs Law_of_cosines.
• Law_of_cosines wasDerivedFrom Law_of_cosines?oldid=602126259.
• Law_of_cosines depiction Triangle_with_notations_2.svg.
• Law_of_cosines isPrimaryTopicOf Law_of_cosines.