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law of cosines

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Wiktionary

  1. law of cosinesnoun

    A statement that relates the lengths of the sides of a triangle to the cosine of one of its angles.

Wikidata

  1. Law of cosines

    In trigonometry, the law of cosines 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 says where 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, 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 are treated separately, in Propositions 12 and 13 of Book 2. Trigonometric functions and algebra being absent in Euclid's time, the statement has a more geometric flavor:

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Numerology

  1. Chaldean Numerology

    The numerical value of law of cosines in Chaldean Numerology is: 7

  2. Pythagorean Numerology

    The numerical value of law of cosines in Pythagorean Numerology is: 6

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"law of cosines." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/law+of+cosines>.

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