# Outline of trigonometry > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Outline_of_trigonometry > Markdown URL: https://mediated.wiki/source/Outline_of_trigonometry.md > Source: https://en.wikipedia.org/wiki/Outline_of_trigonometry > Source revision: 1318180906 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|1=Overview of and topical guide to trigonometry}} {{Trigonometry}} The following [outline](/source/Outline_(list)) is provided as an overview of and topical guide to trigonometry: '''[Trigonometry](/source/Trigonometry)''' – branch of [mathematics](/source/mathematics) that studies the relationships between the sides and the angles in [triangle](/source/triangle)s. Trigonometry defines the [trigonometric functions](/source/trigonometric_functions), which describe those relationships and have applicability to cyclical phenomena, such as [wave](/source/wave)s. {{TOC limit}} == Basics == [[Image:Angle Symbol.svg|thumb|right|∠, the angle symbol in [Unicode](/source/Unicode) is [U+2220](/source/List_of_XML_and_HTML_character_entity_references)|228x228px]] * [Geometry](/source/Geometry) – mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry. * [Angle](/source/Angle) – the angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. * [Ratio](/source/Ratio) – a ratio indicates how many times one number contains another == Content of trigonometry == * [Trigonometry](/source/Trigonometry) * [Trigonometric functions](/source/Trigonometric_functions) * [Trigonometric identities](/source/Trigonometric_identities) * [Euler's formula](/source/Euler's_formula) == Scholars == * [Archimedes](/source/Archimedes) * [Aristarchus](/source/Aristarchus_of_Samos) * [Aryabhata](/source/Aryabhata) * [Bhaskara I](/source/Bhaskara_I) * [Claudius Ptolemy](/source/Claudius_Ptolemy) * [Euclid](/source/Euclid) * [Hipparchus](/source/Hipparchus) * [Madhava of Sangamagrama](/source/Madhava_of_Sangamagrama) * [Ptolemy](/source/Ptolemy) * [Pythagoras](/source/Pythagoras) * [Regiomontanus](/source/Regiomontanus) == History == {{main|Trigonometry#Early history of trigonometry|l1=History of trigonometry}} * [Aristarchus's inequality](/source/Aristarchus's_inequality) * [Bhaskara I's sine approximation formula](/source/Bhaskara_I's_sine_approximation_formula) * [Greek astronomy](/source/Greek_astronomy) * [Indian astronomy](/source/Indian_astronomy) * [Jyā, koti-jyā and utkrama-jyā](/source/Jy%C4%81%2C_koti-jy%C4%81_and_utkrama-jy%C4%81) * [Madhava's sine table](/source/Madhava's_sine_table) * [Ptolemy's table of chords](/source/Ptolemy's_table_of_chords) * [Rule of marteloio](/source/Rule_of_marteloio) * [Āryabhaṭa's sine table](/source/%C4%80ryabha%E1%B9%ADa's_sine_table) == Fields == [Uses of trigonometry](/source/Uses_of_trigonometry) * [Acoustics](/source/Acoustics) * [Architecture](/source/Architecture) * [Astronomy](/source/Astronomy) * [Biology](/source/Biology) * [Cartography](/source/Cartography) * [Chemistry](/source/Chemistry) * [Civil engineering](/source/Civil_engineering) * [Computer graphics](/source/Computer_graphics) * [Cryptography](/source/Cryptography) * [Crystallography](/source/Crystallography) * [Economics](/source/Economics) * [Electrical engineering](/source/Electrical_engineering) * [Electronics](/source/Electronics) * [Game development](/source/Game_development) * [Geodesy](/source/Geodesy) * [Mechanical engineering](/source/Mechanical_engineering) * [Medical imaging](/source/Medical_imaging) * [Meteorology](/source/Meteorology) * [Music theory](/source/Music_theory) * [Number theory](/source/Number_theory) * [Oceanography](/source/Oceanography) * [Optics](/source/Optics) * [Pharmacy](/source/Pharmacy) * [Phonetics](/source/Phonetics) * [Physical science](/source/Outline_of_physical_science) * [Probability theory](/source/Probability_theory) * [Seismology](/source/Seismology) * [Statistics](/source/Statistics) * [Surveying](/source/Surveying) === Physics === * [Abbe sine condition](/source/Abbe_sine_condition) * [Greninger chart](/source/Greninger_chart) * [Phasor](/source/Phasor) * [Snell's law](/source/Snell's_law) === Astronomy === * [Equant](/source/Equant) * [Parallax](/source/Parallax) * [Dialing scales](/source/Dialing_scales) === Chemistry === * [Greninger chart](/source/Greninger_chart) === Geography, geodesy, and land surveying === * [Hansen's problem](/source/Hansen's_problem) * [Snellius–Pothenot problem](/source/Snellius%E2%80%93Pothenot_problem) * [Great-circle distance](/source/Great-circle_distance) – how to find that distance if one knows the [latitude](/source/latitude) and [longitude](/source/longitude). * [Resection (orientation)](/source/Resection_(orientation)) * [Vincenty's formulae](/source/Vincenty's_formulae) * [Geographic distance](/source/Geographic_distance) * [Triangulation in three dimensions](/source/Triangulation_in_three_dimensions) === Navigation === * [Haversine formula](/source/Haversine_formula) * [Rule of marteloio](/source/Rule_of_marteloio) === Engineering === * [Belt problem](/source/Belt_problem) * [Phase response](/source/Phase_response) * [Phasor](/source/Phasor) * [Rake (angle)](/source/Rake_(angle)) === Analog devices === * [Dialing scales](/source/Dialing_scales) * [Gunter's quadrant](/source/Gunter's_quadrant) * [Gunter's scale](/source/Gunter's_scale) * [Protractor](/source/Protractor) * [Scale of chords](/source/Scale_of_chords) == Calculus == * [Inverse trigonometric functions](/source/Inverse_trigonometric_functions) * [List of integrals of trigonometric functions](/source/List_of_integrals_of_trigonometric_functions) * [List of integrals of inverse trigonometric functions](/source/List_of_integrals_of_inverse_trigonometric_functions) * [Regiomontanus' angle maximization problem](/source/Regiomontanus'_angle_maximization_problem) * [Tangent half-angle substitution](/source/Tangent_half-angle_substitution) * [Trigonometric integral](/source/Trigonometric_integral) * [Trigonometric substitution](/source/Trigonometric_substitution) * Applications ** [Fourier transform](/source/Fourier_transform) ** [Wave equation](/source/Wave_equation) == Other areas of mathematics == * For examples of trigonometric functions as [generating functions](/source/generating_functions) in [combinatorics](/source/combinatorics), see [Alternating permutation](/source/Alternating_permutation). * [Dirichlet kernel](/source/Dirichlet_kernel) * [Euler's formula](/source/Euler's_formula) * [Exact trigonometric values](/source/Exact_trigonometric_values) * [Exponential sum](/source/Exponential_sum) * [Trigonometric integral](/source/Trigonometric_integral) * [Trigonometric polynomial](/source/Trigonometric_polynomial) * [Trigonometric series](/source/Trigonometric_series) == Geometric foundations == * [Altern base](/source/Altern_base) * [Angle](/source/Angle) ** [Plane angle](/source/Plane_angle) ** [Solid angle](/source/Solid_angle) ** [Spherical angle](/source/Spherical_angle) ** [Right angle](/source/Right_angle) * [Angle excess](/source/Angle_excess) * [Angular distance](/source/Angular_distance) * [Angular unit](/source/Angular_unit) ** [Degree (angle)](/source/Degree_(angle)) ** [Gon (angle)](/source/Gon_(angle)) (aka Grad, Gradian) ** [Radian](/source/Radian) ** [Turn (angle)](/source/Turn_(angle)) * [Brocard points](/source/Brocard_points) * [Chord (geometry)](/source/Chord_(geometry)) * [Circle](/source/Circle) (also see [List of circle topics](/source/List_of_circle_topics)) ** [Unit circle](/source/Unit_circle) * [Hypotenuse](/source/Hypotenuse) * [Opposites post](/source/Opposites_post) * [{{pi}}](/source/pi) (pi) * [Ptolemy's theorem](/source/Ptolemy's_theorem) * [Pythagorean theorem](/source/Pythagorean_theorem) * [Regiomontanus' angle maximization problem](/source/Regiomontanus'_angle_maximization_problem) * [Thales' theorem](/source/Thales'_theorem) * [Trigonometric function](/source/Trigonometric_function) * [Trigonometry of a tetrahedron](/source/Trigonometry_of_a_tetrahedron) * [Triangle](/source/Triangle) (also see [List of triangle topics](/source/List_of_triangle_topics)) == Trigonometric functions == * [Sine](/source/Sine), [Cosine](/source/Cosine), [Tangent (trigonometric function)](/source/Tangent_(trigonometric_function)), [Cotangent](/source/Cotangent), [Secant (trigonometric function)](/source/Secant_(trigonometric_function)), [Cosecant](/source/Cosecant) – see [Trigonometric function](/source/Trigonometric_function) * [atan2](/source/atan2) * cis—see [Euler's formula](/source/Euler's_formula) * [Cofunction](/source/Cofunction) * [Exsecant](/source/Exsecant) * [Gudermannian function](/source/Gudermannian_function) * [Inverse trigonometric functions](/source/Inverse_trigonometric_functions) * [Jyā, koti-jyā and utkrama-jyā](/source/Jy%C4%81%2C_koti-jy%C4%81_and_utkrama-jy%C4%81) * [Versine](/source/Versine) == Trigonometric identities == [Trigonometric identity](/source/Trigonometric_identity) ([list](/source/List_of_trigonometric_identities)) * [De Moivre's formula](/source/De_Moivre's_formula) * [Euler's formula](/source/Euler's_formula) * [Hermite's cotangent identity](/source/Hermite's_cotangent_identity) * [Lagrange's trigonometric identities](/source/Lagrange's_trigonometric_identities) * [Morrie's law](/source/Morrie's_law) * [Proofs of trigonometric identities](/source/Proofs_of_trigonometric_identities) * [Pythagorean trigonometric identity](/source/Pythagorean_trigonometric_identity) * [Tangent half-angle formula](/source/Tangent_half-angle_formula) == Solution of triangles == [Solution of triangles](/source/Solution_of_triangles) * [Law of sines](/source/Law_of_sines) * [Law of cosines](/source/Law_of_cosines) * [Law of tangents](/source/Law_of_tangents) * [Law of cotangents](/source/Law_of_cotangents) * [Mollweide's formula](/source/Mollweide's_formula) == More advanced trigonometric concepts and methods == * [Chebyshev polynomials](/source/Chebyshev_polynomials) * [Conway triangle notation](/source/Conway_triangle_notation) * [Exact trigonometric constants](/source/Exact_trigonometric_constants) * [Generalized trigonometry](/source/Generalized_trigonometry) * [Gudermannian function](/source/Gudermannian_function) * [Lissajous curve](/source/Lissajous_curve) * [Polar sine](/source/Polar_sine) * [Rational trigonometry](/source/Rational_trigonometry) * [Spread polynomials](/source/Spread_polynomials) == Numerical mathematics == * [Abbe error](/source/Abbe_error) * [Hypot](/source/Hypot) * [Prosthaphaeresis](/source/Prosthaphaeresis) * [Trigonometric interpolation](/source/Trigonometric_interpolation) * [Kunstweg](/source/Kunstweg), an algorithm for computing sines, introduced in the late 1500s === Trigonometric tables === [Trigonometric tables](/source/Trigonometric_tables) * [Generating trigonometric tables](/source/Generating_trigonometric_tables) * [Āryabhaṭa's sine table](/source/%C4%80ryabha%E1%B9%ADa's_sine_table) * [Bhaskara I's sine approximation formula](/source/Bhaskara_I's_sine_approximation_formula) * [Madhava's sine table](/source/Madhava's_sine_table) * [Ptolemy's table of chords](/source/Ptolemy's_table_of_chords), written in the second century A.D. * [Rule of marteloio](/source/Rule_of_marteloio) * [Canon Sinuum](/source/Canon_Sinuum_(B%C3%BCrgi)), listing sines at increments of two arcseconds, published in the late 1500s === Spherical trigonometry === [Spherical trigonometry](/source/Spherical_trigonometry) * [Half-side formula](/source/Half-side_formula) * [Haversine formula](/source/Haversine_formula) == Mnemonics == [mnemonics in trigonometry](/source/mnemonics_in_trigonometry) *[All Students Take Calculus](/source/All_Students_Take_Calculus) == Lists == * [List of integrals of trigonometric functions](/source/List_of_integrals_of_trigonometric_functions) * [List of integrals of inverse trigonometric functions](/source/List_of_integrals_of_inverse_trigonometric_functions) * [List of trigonometric identities](/source/List_of_trigonometric_identities) * [Table of mathematical symbols](/source/Table_of_mathematical_symbols) ==See also== * [Algebra](/source/Algebra) * [Hyperbolic function](/source/Hyperbolic_function) * [List of exponential topics](/source/List_of_exponential_topics) * [Outline of geometry](/source/Outline_of_geometry) * [Precalculus](/source/Precalculus) * [Spherical geometry](/source/Spherical_geometry) * [Table of mathematical symbols](/source/Table_of_mathematical_symbols) == External links == {{Wikibooks|Trigonometry}} * [https://web.archive.org/web/20060924185418/http://www.ping.be/~ping1339/gonio.htm An introduction to trigonometry] * [https://web.archive.org/web/20070930031406/http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=212&bodyId=81 Benjamin Banneker's Trigonometry Puzzle] at [http://mathdl.maa.org/convergence/1/ Convergence] * [http://www.clarku.edu/~djoyce/trig/ Dave's short trig course] {{Webarchive|url=https://web.archive.org/web/20080615133310/http://www.clarku.edu/~djoyce/trig/ |date=2008-06-15 }} * [https://web.archive.org/web/20060414195120/http://www.pupress.princeton.edu/books/maor/ Trigonometric Delights], by [Eli Maor](/source/Eli_Maor), Princeton University Press, 1998. Ebook version, in PDF format, full text presented. * [https://web.archive.org/web/20071104225720/http://baqaqi.chi.il.us/buecher/mathematics/trigonometry/index.html Trigonometry] by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented. * [http://catcode.com/trig/index.html Trigonometry FAQ] * [http://www.mathwords.com/index_trig.htm Trigonometry on Mathwords.com] index of trigonometry entries on Mathwords.com * [http://www.plainmath.net/index.php?page=trig Trigonometry on PlainMath.net] {{Webarchive|url=https://web.archive.org/web/20071027024512/http://www.plainmath.net/index.php?page=trig |date=2007-10-27 }} Trigonometry Articles from PlainMath.Net {{outline footer}} Trigonometry Trigonometry 1 Trigonometry --- Adapted from the Wikipedia article [Outline of trigonometry](https://en.wikipedia.org/wiki/Outline_of_trigonometry) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Outline_of_trigonometry?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.