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Law of sines

Index Law of sines

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles. [1]

46 relations: Absolute value, Abu al-Wafa' Buzjani, Abu Nasr Mansur, Abu-Mahmud Khojandi, Circumscribed circle, Cut-the-Knot, Diameter, Equation, Euclidean space, Face (geometry), Gersonides, Glen Van Brummelen, Half-side formula, Helaine Selin, Heron's formula, Hyperbolic geometry, Hyperbolic triangle, Ibn Muʿādh al-Jayyānī, János Bolyai, Law of cosines, Law of cotangents, Law of tangents, Length, Mollweide's formula, Multiplicative inverse, Nasir al-Din al-Tusi, Normal (geometry), Numerical error, Parallelepiped, Polar sine, Regiomontanus, Semiperimeter, Simplex, Sine, Solution of triangles, Spherical trigonometry, Springer Science+Business Media, Surveying, Tetrahedron, Triangle, Triangulation, Trigonometry, Triple product, Ubiratàn D'Ambrosio, Vertex (geometry), 5-cell.

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Abu al-Wafa' Buzjani

Abū al-Wafāʾ, Muḥammad ibn Muḥammad ibn Yaḥyā ibn Ismāʿīl ibn al-ʿAbbās al-Būzjānī or Abū al-Wafā Būzhjānī (ابوالوفا بوزجانی or بوژگانی) (10 June 940 – 15 July 998) was a Persian mathematician and astronomer who worked in Baghdad.

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Abu Nasr Mansur

Abu Nasri Mansur ibn Ali ibn Iraq (ابو نصر منصور بن علی بن عراق; c. 960 – 1036) was a Persian Muslim mathematician.

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Abu-Mahmud Khojandi

Abu Mahmud Hamid ibn Khidr Khojandi (known as Abu Mahmood Khojandi, Alkhujandi or al-Khujandi, Persian: ابومحمود خجندی, c. 940 - 1000) was a Central Asian astronomer and mathematician who lived in the late 10th century and helped build an observatory, near the city of Ray (near today's Tehran), in Iran.

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Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

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Cut-the-Knot

Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.

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Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

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Equation

In mathematics, an equation is a statement of an equality containing one or more variables.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Gersonides

Levi ben Gershon (1288–1344), better known by his Graecized name as Gersonides or by his Latinized name Magister Leo Hebraeus the abbreviation of first letters as RaLBaG, was a medieval French Jewish philosopher, Talmudist, mathematician, physician and astronomer/astrologer.

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Glen Van Brummelen

Glen Robert Van Brummelen (born 1965) is a Canadian historian of mathematics specializing in historical applications of mathematics to astronomy.

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Half-side formula

In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles.

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Helaine Selin

Helaine Selin (born 1946) is an American librarian, author and the editor of several bestselling books.

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Heron's formula

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

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Hyperbolic geometry

In mathematics, hyperbolic geometry (also called Bolyai–Lobachevskian geometry or Lobachevskian geometry) is a non-Euclidean geometry.

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Hyperbolic triangle

In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane.

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Ibn Muʿādh al-Jayyānī

Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī (989, Cordova, Al-Andalus – 1079, Jaén, Al-Andalus) was a mathematician, Islamic scholar, and Qadi from Al-Andalus (in present-day Spain).

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János Bolyai

János Bolyai (15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, one of the founders of non-Euclidean geometry — a geometry that differs from Euclidean geometry in its definition of parallel lines.

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Law of cosines

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.

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Law of cotangents

In trigonometry, the law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles.

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Law of tangents

In trigonometry, the law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.

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Length

In geometric measurements, length is the most extended dimension of an object.

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Mollweide's formula

In trigonometry, Mollweide's formula, sometimes referred to in older texts as Mollweide's equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle.

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (محمد بن محمد بن حسن طوسی‎ 18 February 1201 – 26 June 1274), better known as Nasir al-Din Tusi (نصیر الدین طوسی; or simply Tusi in the West), was a Persian polymath, architect, philosopher, physician, scientist, and theologian.

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Normal (geometry)

In geometry, a normal is an object such as a line or vector that is perpendicular to a given object.

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Numerical error

In software engineering and mathematics, numerical error is the error in the numerical computations.

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Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

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Polar sine

In geometry, the polar sine generalizes the sine function of angle to the vertex angle of a polytope.

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Regiomontanus

Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus, was a mathematician and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg.

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Semiperimeter

In geometry, the semiperimeter of a polygon is half its perimeter.

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Simplex

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Solution of triangles

Solution of triangles (solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known.

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Spherical trigonometry

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Surveying

Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional positions of points and the distances and angles between them.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Triangulation

In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to it from known points.

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Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

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Triple product

In vector algebra, a branch of mathematics, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors.

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Ubiratàn D'Ambrosio

Ubiratan D'Ambrosio (born December 8, 1932 in São Paulo) is a Brazilian mathematics educator and historian of mathematics.

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Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

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5-cell

In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells.

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Redirects here:

Ambiguous case, Law of Sines, Law of sines (spherical), Law of the sines, Rule of sines, Sin rule, Sine formula, Sine law, Sine rule, Sine theorem, Sines Law, Spherical Law of Sines, Spherical law of sines.

References

[1] https://en.wikipedia.org/wiki/Law_of_sines

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