en.unionpedia.org

Law of cosines, the Glossary

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.^[1]

73 relations: Acute and obtuse triangles, Al-Battani, Al-Biruni, Al-Khwarizmi, Alexander Bogomolny, Altitude (triangle), Angle, Arc length, Area, Binomial theorem, Cartesian coordinate system, Catastrophic cancellation, Chord (geometry), Circle, Congruence (geometry), Converse (logic), Cyclic quadrilateral, Dihedral angle, Divergence theorem, Dot product, Elementary algebra, Euclid, Euclid's Elements, Euclidean distance, Floating-point arithmetic, FOIL method, François Viète, France, Geometry, Great circle, Half-side formula, Haversine formula, Heptagon, Hero of Alexandria, Hexagon, Hyperbolic functions, Hyperbolic geometry, Hyperbolic law of cosines, Intersecting chords theorem, Jamshid al-Kashi, Johannes de Muris, Law of cotangents, Law of sines, Law of tangents, List of trigonometric identities, Mollweide's formula, Nasir al-Din al-Tusi, Negative number, Nilakantha Somayaji, Parallelogram, ... Expand index (23 more) »
Theorems about triangles

Acute and obtuse triangles

An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°).

See Law of cosines and Acute and obtuse triangles

Abū ʿAbd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī aṣ-Ṣābiʾ al-Battānī (محمد بن جابر بن سنان البتاني), usually called al-Battānī, a name that was in the past Latinized as Albategnius, (before 858929) was an astronomer, astrologer and mathematician, who lived and worked for most of his life at Raqqa, now in Syria.

See Law of cosines and Al-Battani

Al-Biruni

Abu Rayhan Muhammad ibn Ahmad al-Biruni (ابوریحان بیرونی; أبو الريحان البيروني; 973after 1050), known as al-Biruni, was a Khwarazmian Iranian scholar and polymath during the Islamic Golden Age.

See Law of cosines and Al-Biruni

Al-Khwarizmi

Muhammad ibn Musa al-Khwarizmi (محمد بن موسى خوارزمی), often referred to as simply al-Khwarizmi, was a polymath who produced vastly influential Arabic-language works in mathematics, astronomy, and geography.

See Law of cosines and Al-Khwarizmi

Alexander Bogomolny

Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli-American mathematician.

See Law of cosines and Alexander Bogomolny

Altitude (triangle)

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex.

See Law of cosines and Altitude (triangle)

Angle

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Law of cosines and angle are trigonometry.

See Law of cosines and Angle

Arc length

Arc length is the distance between two points along a section of a curve.

See Law of cosines and Arc length

Area

Area is the measure of a region's size on a surface.

See Law of cosines and Area

Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

See Law of cosines and Binomial theorem

Cartesian coordinate system

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See Law of cosines and Cartesian coordinate system

Catastrophic cancellation

In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbers.

See Law of cosines and Catastrophic cancellation

Chord (geometry)

A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc.

See Law of cosines and Chord (geometry)

Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

See Law of cosines and Circle

Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

See Law of cosines and Congruence (geometry)

Converse (logic)

In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements.

See Law of cosines and Converse (logic)

Cyclic quadrilateral

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.

See Law of cosines and Cyclic quadrilateral

Dihedral angle

A dihedral angle is the angle between two intersecting planes or half-planes. Law of cosines and dihedral angle are angle.

See Law of cosines and Dihedral angle

Divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem relating the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

See Law of cosines and Divergence theorem

Dot product

In mathematics, the dot product or scalar productThe term scalar product means literally "product with a scalar as a result".

See Law of cosines and Dot product

Elementary algebra

Elementary algebra, also known as college algebra, encompasses the basic concepts of algebra.

See Law of cosines and Elementary algebra

Euclid

Euclid (Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician.

See Law of cosines and Euclid

Euclid's Elements

The Elements (Στοιχεῖα) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid 300 BC.

See Law of cosines and Euclid's Elements

Euclidean distance

In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them.

See Law of cosines and Euclidean distance

Floating-point arithmetic

In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base.

See Law of cosines and Floating-point arithmetic

FOIL method

In elementary algebra, FOIL is a mnemonic for the standard method of multiplying two binomials—hence the method may be referred to as the FOIL method.

See Law of cosines and FOIL method

François Viète

François Viète, Seigneur de la Bigotière (Franciscus Vieta; 1540 – 23 February 1603), commonly known by his mononym, Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to his innovative use of letters as parameters in equations.

See Law of cosines and François Viète

France

France, officially the French Republic, is a country located primarily in Western Europe.

See Law of cosines and France

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Law of cosines and Geometry

Great circle

In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point.

See Law of cosines and Great circle

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.

See Law of cosines and Half-side formula

Haversine formula

The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.

See Law of cosines and Haversine formula

Heptagon

In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.

See Law of cosines and Heptagon

Hero of Alexandria

Hero of Alexandria (Ἥρων ὁ Ἀλεξανδρεύς,, also known as Heron of Alexandria; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era.

See Law of cosines and Hero of Alexandria

Hexagon

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon.

See Law of cosines and Hexagon

Hyperbolic functions

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle.

See Law of cosines and Hyperbolic functions

Hyperbolic geometry

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

See Law of cosines and Hyperbolic geometry

Hyperbolic law of cosines

In hyperbolic geometry, the "law of cosines" is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar law of cosines from plane trigonometry, or the spherical law of cosines in spherical trigonometry.

See Law of cosines and Hyperbolic law of cosines

Intersecting chords theorem

In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.

See Law of cosines and Intersecting chords theorem

Jamshid al-Kashi

Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī) (غیاث الدین جمشید کاشانی Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was an astronomer and mathematician during the reign of Tamerlane.

See Law of cosines and Jamshid al-Kashi

Johannes de Muris

Johannes de Muris (– 1344), or John of Murs, was a French mathematician, astronomer, and music theorist best known for treatises on the ars nova musical style, titled Ars nove musice.

See Law of cosines and Johannes de Muris

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. Law of cosines and law of cotangents are theorems about triangles and trigonometry.

See Law of cosines and Law of cotangents

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 any triangle to the sines of its angles. Law of cosines and law of sines are angle, theorems about triangles and trigonometry.

See Law of cosines and Law of sines

Law of tangents

In trigonometry, the law of tangents or tangent rule is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. Law of cosines and law of tangents are theorems about triangles and trigonometry.

See Law of cosines and Law of tangents

List of trigonometric identities

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Law of cosines and List of trigonometric identities are trigonometry.

See Law of cosines and List of trigonometric identities

Mollweide's formula

In trigonometry, Mollweide's formula is a pair of relationships between sides and angles in a triangle. Law of cosines and Mollweide's formula are theorems about triangles and trigonometry.

See Law of cosines and Mollweide's formula

Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tusi (1201 – 1274), also known as Nasir al-Din al-Tusi (نصیر الدین الطوسی; نصیر الدین طوسی) or simply as (al-)Tusi, was a Persian polymath, architect, philosopher, physician, scientist, and theologian.

See Law of cosines and Nasir al-Din al-Tusi

Negative number

In mathematics, a negative number represents an opposite.

See Law of cosines and Negative number

Nilakantha Somayaji

Keļallur Nīlakaṇṭha Somayāji (14 June 1444 – 1544), also referred to as Keļallur Comatiri, was a major mathematician and astronomer of the Kerala school of astronomy and mathematics.

See Law of cosines and Nilakantha Somayaji

Parallelogram

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.

See Law of cosines and Parallelogram

Perpendicular

In geometry, two geometric objects are perpendicular if their intersection forms right angles (angles that are 90 degrees or π/2 radians wide) at the point of intersection called a foot.

See Law of cosines and Perpendicular

Polyhedron

In geometry, a polyhedron (polyhedra or polyhedrons) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.

See Law of cosines and Polyhedron

Polynomial expansion

In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition.

See Law of cosines and Polynomial expansion

Power of a point

In elementary plane geometry, the power of a point is a real number that reflects the relative distance of a given point from a given circle.

See Law of cosines and Power of a point

Ptolemy's theorem

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

See Law of cosines and Ptolemy's theorem

Pythagorean theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. Law of cosines and Pythagorean theorem are angle.

See Law of cosines and Pythagorean theorem

Pythagorean trigonometric identity

The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Law of cosines and Pythagorean trigonometric identity are trigonometry.

See Law of cosines and Pythagorean trigonometric identity

Quadratic equation

In mathematics, a quadratic equation is an equation that can be rearranged in standard form as ax^2 + bx + c.

See Law of cosines and Quadratic equation

Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or radians corresponding to a quarter turn. Law of cosines and right angle are angle.

See Law of cosines and Right angle

Right triangle

A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular forming a right angle (turn or 90 degrees).

See Law of cosines and Right triangle

Round-off error

In computing, a roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic.

See Law of cosines and Round-off error

Secant line

In geometry, a secant is a line that intersects a curve at a minimum of two distinct points.

See Law of cosines and Secant line

Sine and cosine

In mathematics, sine and cosine are trigonometric functions of an angle. Law of cosines and sine and cosine are angle.

See Law of cosines and Sine and cosine

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. Law of cosines and Solution of triangles are trigonometry.

See Law of cosines and Solution of triangles

Special case

In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of.

See Law of cosines and Special case

Spherical geometry

A sphere with a spherical triangle on it. Spherical geometry or spherics is the geometry of the two-dimensional surface of a sphere or the -dimensional surface of higher dimensional spheres.

See Law of cosines and Spherical geometry

Spherical law of cosines

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.

See Law of cosines and Spherical law of cosines

Tangent–secant theorem

In Euclidean geometry, the tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle.

See Law of cosines and Tangent–secant theorem

Tetrahedron

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

See Law of cosines and Tetrahedron

Thomas Heath (classicist)

Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer.

See Law of cosines and Thomas Heath (classicist)

Triangle

A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry.

See Law of cosines and Triangle

Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. Law of cosines and trigonometric functions are angle and trigonometry.

See Law of cosines and Trigonometric functions

Trigonometry

Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles.

See Law of cosines and Trigonometry

References

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

Also known as Al Kashi formula, Al-Kashi's theorem, Cos law, Cos rule, Cosine Law, Cosine Rule, Cosine formula, Cosine relation, Cosine theorem, Cosines law, Law of cos, Law of cosine, Laws of cosines, The Law of Cosines.

, Perpendicular, Polyhedron, Polynomial expansion, Power of a point, Ptolemy's theorem, Pythagorean theorem, Pythagorean trigonometric identity, Quadratic equation, Right angle, Right triangle, Round-off error, Secant line, Sine and cosine, Solution of triangles, Special case, Spherical geometry, Spherical law of cosines, Tangent–secant theorem, Tetrahedron, Thomas Heath (classicist), Triangle, Trigonometric functions, Trigonometry.

Law of cosines, the Glossary

Table of Contents

See also

Theorems about triangles

References