law of cosines
- Trigonom.1. a law stating that the square of a side of a plane triangle is equal to the sum of the squares of the other two sides minus twice the product of the other sides multiplied by the cosine of the angle between them.2. a law stating that the cosine of an arc of a spherical triangle equals the sum of the product of the cosines of the other two arcs added to the product of the sines of the other two arcs multiplied by the cosine of the angle between them.
* * *Generalization of the Pythagorean theorem relating the lengths of the sides of any triangle.If a, b, and c are the lengths of the sides and C is the angle opposite side c, then c2 = a2 + b2 -2ab cos C.
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Law of cosines — This article is about the law of cosines in Euclidean geometry. For the cosine law of optics, see Lambert s cosine law. Figure 1 – A triangle. The angles α, β, and γ are respectively opposite the sides a, b, and c … Wikipedia
law of cosines — 1. : a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them 2. : a law in trigonometry: the cosine of an … Useful english dictionary
law of cosines — noun A statement that relates the lengths of the sides of a triangle to the cosine of one of its angles. Syn: cosine formula, cosine rule … Wiktionary
Law of cosines (spherical) — In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry.Given a unit sphere, a… … Wikipedia
Law — /law/, n. 1. Andrew Bonar /bon euhr/, 1858 1923, English statesman, born in Canada: prime minister 1922 23. 2. John, 1671 1729, Scottish financier. 3. William, 1686 1761, English clergyman and devotional writer. * * * I Discipline and profession… … Universalium
Law of tangents — In trigonometry, the law of tangents is a statement about the relationship between the lengths of the three sides of a triangle and the tangents of the angles.In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α,… … Wikipedia
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Law of sines — The law of sines (sines law, sine formula, sine rule), in trigonometry, is a statement about any triangle in a plane. Where the sides of the triangle are a , b and c and the angles opposite those sides are A , B and C , then the law of sines… … Wikipedia
hyperbolic cosines — Hyperbolic Hy per*bol ic, Hyperbolical Hy per*bol ic*al, a. [L. hyperbolicus, Gr. ?: cf. F. hyperbolique.] 1. (Math.) Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster] 2. (Rhet.) Relating to, containing, or of the… … The Collaborative International Dictionary of English
Benford's law — Benford s law, also called the first digit law, states that in lists of numbers from many real life sources of data, the leading digit is distributed in a specific, non uniform way. According to this law, the first digit is 1 almost one third of… … Wikipedia