Trigonometry is a branch of mathematics concerned with the relationships between the angles and side lengths of triangles, with its trigonometric functions relating the angles of a right triangle to the ratios of its sides. The discipline developed in the Hellenistic period around the third century BC out of geometric methods applied to astronomy, and Indian mathematicians later produced the first known tables of trigonometric ratios such as the sine.
Facts
Central QuestionTrigonometry asks how the angles and side lengths of triangles relate to one another, and how those relationships can be captured as functions usable for computation in astronomy, navigation and surveying. 1 Key DebateHistorians dispute where trigonometry as its own independent mathematical discipline actually began, whether with the chord tables the Hellenistic Greeks Hipparchus and Ptolemy built for astronomy, or only later with the Persian polymath Nasir al-Din al-Tusi, who has been credited as the first to treat it as a discipline separate from astronomy. 1 Classification
Pure or AppliedBoth / Interdisciplinary 1 Trigonometry
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Associated With
Source Trigonometry (Wikipedia)
Includes
Source Wolfram MathWorld: Angle Trisection
Source De Moivre's formula (Wikipedia)
Source Differentiation of Trigonometric Functions (Wikipedia)
Source Haversine Formula (Wikipedia)
Source MacTutor biography of Hipparchus, St Andrews
Source Pythagorean trigonometric identity (Wikipedia)
Sources
1. Trigonometry (Wikipedia)
Wikimedia FoundationLead section
Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
History section, Nasir al-Din al-Tusi passage
The Persian polymath Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right. He was the first to treat trigonometry as a mathematical discipline independent from astronomy, and he developed spherical trigonometry into its present form.
Associated With: Geometry, Wikipedia lead paragraph, Trigonometry
The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
View the Source Haversine Formula (Wikipedia)
Includes: Haversine formula, Lead paragraphQuote, Includes: Haversine formula, Lead paragraph
Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
De Moivre's formula (Wikipedia)
Includes: De Moivre's Formula, Lead paragraphQuote, Includes: De Moivre's Formula, Lead paragraph
The formula is important because it connects complex numbers and trigonometry.
Wolfram MathWorld: Angle Trisection
Wolfram MathWorldIncludes: Angle Trisection, Subject classificationsQuote, Includes: Angle Trisection, Subject classifications
Geometry Trigonometry
Pythagorean trigonometric identity (Wikipedia)
Includes: Pythagorean Trigonometric Identity, Lead sectionQuote, Includes: Pythagorean Trigonometric Identity, Lead section
The Pythagorean trigonometric identity, also called simply the Pythagorean
Differentiation of Trigonometric Functions (Wikipedia)
Includes: Differentiation of Trigonometric Functions, Lead sectionQuote, Includes: Differentiation of Trigonometric Functions, Lead section
The differentiation of trigonometric functions is the mathematical process of finding
MacTutor biography of Hipparchus, St Andrews
Includes: Hipparchus, SummaryQuote, Includes: Hipparchus, Summary
Hipparchus was a Greek mathematician who compiled an early example of trigonometric tables and gave methods for solving spherical triangles.
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