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Outline of trigonometry
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<h2 id="basics">Basics</h2> <ul><li><a href="/facts/Geometry/wTQf5ffQ">Geometry</a> – mathematics concerned with questions of shape, size, the relative position of figures, and the properties of space. Geometry is used extensively in trigonometry.</li> <li><a href="/facts/Angle/gFUTEQYq">Angle</a> – 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.</li> <li><a href="/facts/Ratio/mFmhQt7T">Ratio</a> – a ratio indicates how many times one number contains another</li></ul> <h2 id="content-of-trigonometry">Content of trigonometry</h2> <ul><li><a href="/facts/Trigonometry/K4hfaC6F">Trigonometry</a></li> <li><a href="/facts/Trigonometric_functions/czej7ur0">Trigonometric functions</a></li> <li><a href="/facts/Trigonometric_identities/Xw9Jx8Vz">Trigonometric identities</a></li> <li><a href="/facts/Euler%2527s_formula/Wq7VXIV0">Euler's formula</a></li></ul> <h2 id="scholars">Scholars</h2> <ul><li><a href="/facts/Archimedes/sIeMhSVF">Archimedes</a></li> <li><a href="/facts/Aristarchus_of_Samos/cyfJR02u">Aristarchus</a></li> <li><a href="/facts/Aryabhata/3L1j5TDm">Aryabhata</a></li> <li><a href="/facts/Bhaskara_I/aXwgEgnQ">Bhaskara I</a></li> <li><a href="/facts/Claudius_Ptolemy/htudGQTQ">Claudius Ptolemy</a></li> <li><a href="/facts/Euclid/dHpVyL4R">Euclid</a></li> <li><a href="/facts/Hipparchus/pHld5PfE">Hipparchus</a></li> <li><a href="/facts/Madhava_of_Sangamagrama/09hFJnVQ">Madhava of Sangamagrama</a></li> <li><a href="/facts/Ptolemy/htudGQTQ">Ptolemy</a></li> <li><a href="/facts/Pythagoras/8oe8UgCj">Pythagoras</a></li> <li><a href="/facts/Regiomontanus/CrMSdtQU">Regiomontanus</a></li></ul> <h2 id="history">History</h2> <p class="note">Main article: <a href="/facts/Trigonometry/K4hfaC6F">History of trigonometry</a></p> <ul><li><a href="/facts/Aristarchus%2527s_inequality/tdGFfR5e">Aristarchus's inequality</a></li> <li><a href="/facts/Bhaskara_I%2527s_sine_approximation_formula/4Br4KU52">Bhaskara I's sine approximation formula</a></li> <li><a href="/facts/Greek_astronomy/ehwqftGz">Greek astronomy</a></li> <li><a href="/facts/Indian_astronomy/q9pgvuCm">Indian astronomy</a></li> <li><a href="/facts/Jy%25C4%2581%2c_koti-jy%25C4%2581_and_utkrama-jy%25C4%2581/Nn4zMtM1">Jyā, koti-jyā and utkrama-jyā</a></li> <li><a href="/facts/Madhava%2527s_sine_table/3KDWEd0o">Madhava's sine table</a></li> <li><a href="/facts/Ptolemy%2527s_table_of_chords/h6Ubj0sq">Ptolemy's table of chords</a></li> <li><a href="/facts/Rule_of_marteloio/yUbQRQBW">Rule of marteloio</a></li> <li><a href="/facts/%25C4%2580ryabha%25E1%25B9%25ADa%2527s_sine_table/HcDsEuDj">Āryabhaṭa's sine table</a></li></ul> <h2 id="fields">Fields</h2> <p><a href="/facts/Uses_of_trigonometry/H6JuC55m">Uses of trigonometry</a> </p> <ul><li><a href="/facts/Acoustics/2GpQUymy">Acoustics</a></li> <li><a href="/facts/Architecture/FccThs8G">Architecture</a></li> <li><a href="/facts/Astronomy/0ArJVM1p">Astronomy</a></li> <li><a href="/facts/Biology/1M1ee3pB">Biology</a></li> <li><a href="/facts/Cartography/8YdDAAeX">Cartography</a></li> <li><a href="/facts/Chemistry/SrNqkGVm">Chemistry</a></li> <li><a href="/facts/Civil_engineering/avh5kEq2">Civil engineering</a></li> <li><a href="/facts/Computer_graphics/lapBE8wv">Computer graphics</a></li> <li><a href="/facts/Cryptography/e94PEVau">Cryptography</a></li> <li><a href="/facts/Crystallography/9B5toeqG">Crystallography</a></li> <li><a href="/facts/Economics/HYctA2Dn">Economics</a></li> <li><a href="/facts/Electrical_engineering/YYXW1KLW">Electrical engineering</a></li> <li><a href="/facts/Electronics/E4JhgISq">Electronics</a></li> <li><a href="/facts/Game_development/bzbpfYJd">Game development</a></li> <li><a href="/facts/Geodesy/EJH0Te0m">Geodesy</a></li> <li><a href="/facts/Mechanical_engineering/cbId4fye">Mechanical engineering</a></li> <li><a href="/facts/Medical_imaging/pL6JyJEp">Medical imaging</a></li> <li><a href="/facts/Meteorology/xblFr28q">Meteorology</a></li> <li><a href="/facts/Music_theory/BoekvflP">Music theory</a></li> <li><a href="/facts/Number_theory/zhoa7zrc">Number theory</a></li> <li><a href="/facts/Oceanography/LtrG6peD">Oceanography</a></li> <li><a href="/facts/Optics/p0vq4S1T">Optics</a></li> <li><a href="/facts/Pharmacy/P2KTFVdW">Pharmacy</a></li> <li><a href="/facts/Phonetics/ljAVT8fv">Phonetics</a></li> <li><a href="/facts/Outline_of_physical_science/30ztjEKK">Physical science</a></li> <li><a href="/facts/Probability_theory/mFBn51rE">Probability theory</a></li> <li><a href="/facts/Seismology/Lony1LYX">Seismology</a></li> <li><a href="/facts/Statistics/DNPsKGYU">Statistics</a></li> <li><a href="/facts/Surveying/qchGcnRC">Surveying</a></li></ul> <h3>Physics</h3> <ul><li><a href="/facts/Abbe_sine_condition/bq7EwqIN">Abbe sine condition</a></li> <li><a href="/facts/Greninger_chart/fUksVuEj">Greninger chart</a></li> <li><a href="/facts/Phasor/LyjSSUDo">Phasor</a></li> <li><a href="/facts/Snell%2527s_law/cE0rhDXd">Snell's law</a></li></ul> <h3>Astronomy</h3> <ul><li><a href="/facts/Equant/Eq942l8h">Equant</a></li> <li><a href="/facts/Parallax/Gu8W21LP">Parallax</a></li> <li><a href="/facts/Dialing_scales/JmokdH1n">Dialing scales</a></li></ul> <h3>Chemistry</h3> <ul><li><a href="/facts/Greninger_chart/fUksVuEj">Greninger chart</a></li></ul> <h3>Geography, geodesy, and land surveying</h3> <ul><li><a href="/facts/Hansen%2527s_problem/7NnRaSyR">Hansen's problem</a></li> <li><a href="/facts/Snellius%25E2%2580%2593Pothenot_problem/UMHQ2wRk">Snellius–Pothenot problem</a></li> <li><a href="/facts/Great-circle_distance/s6HNWn8e">Great-circle distance</a> – how to find that distance if one knows the <a href="/facts/Latitude/IBYqkjhU">latitude</a> and <a href="/facts/Longitude/HsC61ML9">longitude</a>.</li> <li><a href="/facts/Resection_(orientation)/EhURl1K3">Resection (orientation)</a></li> <li><a href="/facts/Vincenty%2527s_formulae/Rg491HTb">Vincenty's formulae</a></li> <li><a href="/facts/Geographic_distance/r0a5tbgV">Geographic distance</a></li> <li><a href="/facts/Triangulation_in_three_dimensions/lpmlmhGd">Triangulation in three dimensions</a></li></ul> <h3>Navigation</h3> <ul><li><a href="/facts/Haversine_formula/NGJlq4q7">Haversine formula</a></li> <li><a href="/facts/Rule_of_marteloio/yUbQRQBW">Rule of marteloio</a></li></ul> <h3>Engineering</h3> <ul><li><a href="/facts/Belt_problem/aewzWcTA">Belt problem</a></li> <li><a href="/facts/Phase_response/xnT0b9mE">Phase response</a></li> <li><a href="/facts/Phasor/LyjSSUDo">Phasor</a></li> <li><a href="/facts/Rake_(angle)/C4LRSUjq">Rake (angle)</a></li></ul> <h3>Analog devices</h3> <ul><li><a href="/facts/Dialing_scales/JmokdH1n">Dialing scales</a></li> <li><a href="/facts/Gunter%2527s_quadrant/wMA91AKt">Gunter's quadrant</a></li> <li><a href="/facts/Gunter%2527s_scale/wMA91AKt">Gunter's scale</a></li> <li><a href="/facts/Protractor/6INTgy5h">Protractor</a></li> <li><a href="/facts/Scale_of_chords/hSJhVkUH">Scale of chords</a></li></ul> <h2 id="calculus">Calculus</h2> <ul><li><a href="/facts/Inverse_trigonometric_functions/bVwU9FPG">Inverse trigonometric functions</a></li> <li><a href="/facts/List_of_integrals_of_trigonometric_functions/lPygFUJk">List of integrals of trigonometric functions</a></li> <li><a href="/facts/List_of_integrals_of_inverse_trigonometric_functions/z725Ym5w">List of integrals of inverse trigonometric functions</a></li> <li><a href="/facts/Regiomontanus%2527_angle_maximization_problem/CBRjKwjT">Regiomontanus' angle maximization problem</a></li> <li><a href="/facts/Tangent_half-angle_substitution/3up24fUw">Tangent half-angle substitution</a></li> <li><a href="/facts/Trigonometric_integral/JB75EqnB">Trigonometric integral</a></li> <li><a href="/facts/Trigonometric_substitution/U6LBLAYU">Trigonometric substitution</a></li> <li>Applications <ul><li><a href="/facts/Fourier_transform/XXhKJtc8">Fourier transform</a></li> <li><a href="/facts/Wave_equation/J2ksD2Az">Wave equation</a></li></ul></li></ul> <h2 id="other-areas-of-mathematics">Other areas of mathematics</h2> <ul><li>For examples of trigonometric functions as <a href="/facts/Generating_functions/K7UVjnjL">generating functions</a> in <a href="/facts/Combinatorics/k14xUoKT">combinatorics</a>, see <a href="/facts/Alternating_permutation/Fl7tSe9z">Alternating permutation</a>.</li> <li><a href="/facts/Dirichlet_kernel/eKdT65eP">Dirichlet kernel</a></li> <li><a href="/facts/Euler%2527s_formula/Wq7VXIV0">Euler's formula</a></li> <li><a href="/facts/Exact_trigonometric_values/zYE1BVLF">Exact trigonometric values</a></li> <li><a href="/facts/Exponential_sum/FRljcVtv">Exponential sum</a></li> <li><a href="/facts/Trigonometric_integral/JB75EqnB">Trigonometric integral</a></li> <li><a href="/facts/Trigonometric_polynomial/K2FEr7Ic">Trigonometric polynomial</a></li> <li><a href="/facts/Trigonometric_series/8SqloJ2z">Trigonometric series</a></li></ul> <h2 id="geometric-foundations">Geometric foundations</h2> <ul><li>Altern base</li> <li><a href="/facts/Angle/gFUTEQYq">Angle</a> <ul><li><a href="/facts/Plane_angle/gFUTEQYq">Plane angle</a></li> <li><a href="/facts/Solid_angle/se8IXufg">Solid angle</a></li> <li><a href="/facts/Spherical_angle/ekVT5dW2">Spherical angle</a></li> <li><a href="/facts/Right_angle/psaslRq7">Right angle</a></li></ul></li> <li><a href="/facts/Angle_excess/3G3Fhk2h">Angle excess</a></li> <li><a href="/facts/Angular_distance/6ob2n0Wb">Angular distance</a></li> <li><a href="/facts/Angular_unit/YbEBfawp">Angular unit</a> <ul><li><a href="/facts/Degree_(angle)/f48Ns8SX">Degree (angle)</a></li> <li><a href="/facts/Gon_(angle)/FoTX1r68">Gon (angle)</a> (aka Grad, Gradian)</li> <li><a href="/facts/Radian/Srd38Sxa">Radian</a></li> <li><a href="/facts/Turn_(angle)/QczxAyuM">Turn (angle)</a></li></ul></li> <li><a href="/facts/Brocard_points/zMXWMQY8">Brocard points</a></li> <li><a href="/facts/Chord_(geometry)/aAyoEdLd">Chord (geometry)</a></li> <li><a href="/facts/Circle/9fy5ggKn">Circle</a> (also see <a href="/facts/List_of_circle_topics/2ll5kjaL">List of circle topics</a>) <ul><li><a href="/facts/Unit_circle/VsTffjPK">Unit circle</a></li></ul></li> <li><a href="/facts/Hypotenuse/hVMauM5f">Hypotenuse</a></li> <li>Opposites post</li> <li><a href="/facts/Pi/vC0UBj1q">π</a> (pi)</li> <li><a href="/facts/Ptolemy%2527s_theorem/sGT3qbh5">Ptolemy's theorem</a></li> <li><a href="/facts/Pythagorean_theorem/Lh6x2Kr5">Pythagorean theorem</a></li> <li><a href="/facts/Regiomontanus%2527_angle_maximization_problem/CBRjKwjT">Regiomontanus' angle maximization problem</a></li> <li><a href="/facts/Thales%2527_theorem/wI6hpFFk">Thales' theorem</a></li> <li><a href="/facts/Trigonometric_function/czej7ur0">Trigonometric function</a></li> <li><a href="/facts/Trigonometry_of_a_tetrahedron/2qMhRdRh">Trigonometry of a tetrahedron</a></li> <li><a href="/facts/Triangle/cRXUwsMn">Triangle</a> (also see <a href="/facts/List_of_triangle_topics/09HL0IlH">List of triangle topics</a>)</li></ul> <h2 id="trigonometric-functions">Trigonometric functions</h2> <ul><li><a href="/facts/Sine/gQ6LXK8z">Sine</a>, <a href="/facts/Cosine/czej7ur0">Cosine</a>, <a href="/facts/Tangent_(trigonometric_function)/czej7ur0">Tangent (trigonometric function)</a>, <a href="/facts/Cotangent/czej7ur0">Cotangent</a>, <a href="/facts/Secant_(trigonometric_function)/czej7ur0">Secant (trigonometric function)</a>, <a href="/facts/Cosecant/czej7ur0">Cosecant</a> – see <a href="/facts/Trigonometric_function/czej7ur0">Trigonometric function</a></li> <li><a href="/facts/Atan2/0JDnUYfP">atan2</a></li> <li>cis—see <a href="/facts/Euler%2527s_formula/Wq7VXIV0">Euler's formula</a></li> <li><a href="/facts/Cofunction/FWLYWR5V">Cofunction</a></li> <li><a href="/facts/Exsecant/CNKrYMjC">Exsecant</a></li> <li><a href="/facts/Gudermannian_function/bA0B2KcC">Gudermannian function</a></li> <li><a href="/facts/Inverse_trigonometric_functions/bVwU9FPG">Inverse trigonometric functions</a></li> <li><a href="/facts/Jy%25C4%2581%2c_koti-jy%25C4%2581_and_utkrama-jy%25C4%2581/Nn4zMtM1">Jyā, koti-jyā and utkrama-jyā</a></li> <li><a href="/facts/Versine/MllE4ISd">Versine</a></li></ul> <h2 id="trigonometric-identities">Trigonometric identities</h2> <p><a href="/facts/Trigonometric_identity/Xw9Jx8Vz">Trigonometric identity</a> (<a href="/facts/List_of_trigonometric_identities/Xw9Jx8Vz">list</a>) </p> <ul><li><a href="/facts/De_Moivre%2527s_formula/uyG4k2uC">De Moivre's formula</a></li> <li><a href="/facts/Euler%2527s_formula/Wq7VXIV0">Euler's formula</a></li> <li><a href="/facts/Hermite%2527s_cotangent_identity/HJ4qA6u3">Hermite's cotangent identity</a></li> <li><a href="/facts/Lagrange%2527s_trigonometric_identities/Xw9Jx8Vz">Lagrange's trigonometric identities</a></li> <li><a href="/facts/Morrie%2527s_law/WYqsC3mH">Morrie's law</a></li> <li><a href="/facts/Proofs_of_trigonometric_identities/7NH0qKLw">Proofs of trigonometric identities</a></li> <li><a href="/facts/Pythagorean_trigonometric_identity/MQsE3Qhc">Pythagorean trigonometric identity</a></li> <li><a href="/facts/Tangent_half-angle_formula/p5ph5VWu">Tangent half-angle formula</a></li></ul> <h2 id="solution-of-triangles">Solution of triangles</h2> <p><a href="/facts/Solution_of_triangles/Dx8AK9bp">Solution of triangles</a> </p> <ul><li><a href="/facts/Law_of_sines/PXNDVjlN">Law of sines</a></li> <li><a href="/facts/Law_of_cosines/RRTGcW0V">Law of cosines</a></li> <li><a href="/facts/Law_of_tangents/UFJKpkQX">Law of tangents</a></li> <li><a href="/facts/Law_of_cotangents/X1qcgBcV">Law of cotangents</a></li> <li><a href="/facts/Mollweide%2527s_formula/jaIhX5gJ">Mollweide's formula</a></li></ul> <h2 id="more-advanced-trigonometric-concepts-and-methods">More advanced trigonometric concepts and methods</h2> <ul><li><a href="/facts/Chebyshev_polynomials/HoBINqgC">Chebyshev polynomials</a></li> <li><a href="/facts/Conway_triangle_notation/89e0er7p">Conway triangle notation</a></li> <li><a href="/facts/Exact_trigonometric_constants/J3g7bxW0">Exact trigonometric constants</a></li> <li><a href="/facts/Generalized_trigonometry/RW9EzmSQ">Generalized trigonometry</a></li> <li><a href="/facts/Gudermannian_function/bA0B2KcC">Gudermannian function</a></li> <li><a href="/facts/Lissajous_curve/vbsovdjN">Lissajous curve</a></li> <li><a href="/facts/Polar_sine/jQX6jaCV">Polar sine</a></li> <li><a href="/facts/Rational_trigonometry/snPXwouV">Rational trigonometry</a></li> <li><a href="/facts/Spread_polynomials/snPXwouV">Spread polynomials</a></li></ul> <h2 id="numerical-mathematics">Numerical mathematics</h2> <ul><li><a href="/facts/Abbe_error/DKlyLmUR">Abbe error</a></li> <li><a href="/facts/Hypot/yxbWdhqu">Hypot</a></li> <li><a href="/facts/Prosthaphaeresis/u1FKPxpj">Prosthaphaeresis</a></li> <li><a href="/facts/Trigonometric_interpolation/CBpDzKwL">Trigonometric interpolation</a></li> <li><a href="/facts/Kunstweg/BD6dCVIu">Kunstweg</a>, an algorithm for computing sines, introduced in the late 1500s</li></ul> <h3>Trigonometric tables</h3> <p><a href="/facts/Trigonometric_tables/LDUT4L9B">Trigonometric tables</a> </p> <ul><li><a href="/facts/Generating_trigonometric_tables/LDUT4L9B">Generating trigonometric tables</a></li> <li><a href="/facts/%25C4%2580ryabha%25E1%25B9%25ADa%2527s_sine_table/HcDsEuDj">Āryabhaṭa's sine table</a></li> <li><a href="/facts/Bhaskara_I%2527s_sine_approximation_formula/4Br4KU52">Bhaskara I's sine approximation formula</a></li> <li><a href="/facts/Madhava%2527s_sine_table/3KDWEd0o">Madhava's sine table</a></li> <li><a href="/facts/Ptolemy%2527s_table_of_chords/h6Ubj0sq">Ptolemy's table of chords</a>, written in the second century A.D.</li> <li><a href="/facts/Rule_of_marteloio/yUbQRQBW">Rule of marteloio</a></li> <li><a href="/facts/Canon_Sinuum_(B%25C3%25BCrgi)/d67yFVyx">Canon Sinuum</a>, listing sines at increments of two arcseconds, published in the late 1500s</li></ul> <h3>Spherical trigonometry</h3> <p><a href="/facts/Spherical_trigonometry/3G3Fhk2h">Spherical trigonometry</a> </p> <ul><li><a href="/facts/Half-side_formula/Bf82DjGo">Half-side formula</a></li> <li><a href="/facts/Haversine_formula/NGJlq4q7">Haversine formula</a></li></ul> <h2 id="mnemonics">Mnemonics</h2> <p><a href="/facts/Mnemonics_in_trigonometry/tfIrN7IP">mnemonics in trigonometry</a> </p> <ul><li><a href="/facts/All_Students_Take_Calculus/tfIrN7IP">All Students Take Calculus</a></li></ul> <h2 id="lists">Lists</h2> <ul><li><a href="/facts/List_of_integrals_of_trigonometric_functions/lPygFUJk">List of integrals of trigonometric functions</a></li> <li><a href="/facts/List_of_integrals_of_inverse_trigonometric_functions/z725Ym5w">List of integrals of inverse trigonometric functions</a></li> <li><a href="/facts/List_of_trigonometric_identities/Xw9Jx8Vz">List of trigonometric identities</a></li> <li><a href="/facts/Table_of_mathematical_symbols/rQkbGGna">Table of mathematical symbols</a></li></ul> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Algebra/nMdqczjo">Algebra</a></li> <li><a href="/facts/Hyperbolic_function/Y4Cb5S35">Hyperbolic function</a></li> <li><a href="/facts/List_of_exponential_topics/TNgs72qw">List of exponential topics</a></li> <li><a href="/facts/Outline_of_geometry/qtfa2Uby">Outline of geometry</a></li> <li><a href="/facts/Precalculus/5RAmBssd">Precalculus</a></li> <li><a href="/facts/Spherical_geometry/WGLQb1Ys">Spherical geometry</a></li> <li><a href="/facts/Table_of_mathematical_symbols/rQkbGGna">Table of mathematical symbols</a></li></ul> <h2 id="external-links">External links</h2> Wikibooks has a book on the topic of: <i>Trigonometry</i> <ul><li><a href="https://web.archive.org/web/20060924185418/http://www.ping.be/~ping1339/gonio.htm">An introduction to trigonometry</a></li> <li><a href="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</a> at <a href="http://mathdl.maa.org/convergence/1/">Convergence</a></li> <li><a href="http://www.clarku.edu/~djoyce/trig/">Dave's short trig course</a></li> <li><a href="https://web.archive.org/web/20060414195120/http://www.pupress.princeton.edu/books/maor/">Trigonometric Delights</a>, by <a href="/facts/Eli_Maor/sTbytsj0">Eli Maor</a>, Princeton University Press, 1998. Ebook version, in PDF format, full text presented.</li> <li><a href="https://web.archive.org/web/20071104225720/http://baqaqi.chi.il.us/buecher/mathematics/trigonometry/index.html">Trigonometry</a> by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented.</li> <li><a href="http://catcode.com/trig/index.html">Trigonometry FAQ</a></li> <li><a href="http://www.mathwords.com/index_trig.htm">Trigonometry on Mathwords.com</a> index of trigonometry entries on Mathwords.com</li> <li><a href="http://www.plainmath.net/index.php?page=trig">Trigonometry on PlainMath.net</a> Trigonometry Articles from PlainMath.Net</li></ul>