Outline of trigonometry

The following outline is provided as an overview of and topical guide to trigonometry:

Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.

Basics

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 – 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 – a ratio indicates how many times one number contains another

Content of trigonometry Trigonometry Trigonometric functions Trigonometric identities Euler's formula

Scholars

Archimedes Aristarchus Aryabhata Bhaskara I Claudius Ptolemy Euclid Hipparchus Madhava of Sangamagrama Ptolemy Pythagoras Regiomontanus

History

Aristarchus's inequality Bhaskara I's sine approximation formula Greek astronomy Indian astronomy Jyā, koti-jyā and utkrama-jyā Madhava's sine table Ptolemy's table of chords Rule of marteloio Āryabhaṭa's sine table

Fields

Uses of trigonometry Acoustics Architecture Astronomy Biology Cartography Chemistry Civil engineering Computer graphics Cryptography Crystallography Economics Electrical engineering Electronics Game development Geodesy Mechanical engineering Medical imaging Meteorology Music theory Number theory Oceanography Optics Pharmacy Phonetics Physical science Probability theory Seismology Statistics Surveying

Physics

Abbe sine condition Greninger chart Phasor Snell's law

Astronomy

Equant Parallax Dialing scales

Chemistry

Greninger chart

Geography, geodesy, and land surveying

Hansen's problem Snellius–Pothenot problem Great-circle distance – how to find that distance if one knows the latitude and longitude. Resection (orientation) Vincenty's formulae Geographic distance Triangulation in three dimensions

Navigation

Haversine formula Rule of marteloio

Engineering

Belt problem Phase response Phasor Rake (angle)

Analog devices

Dialing scales Gunter's quadrant Gunter's scale Protractor Scale of chords

Calculus

Inverse trigonometric functions List of integrals of trigonometric functions List of integrals of inverse trigonometric functions Regiomontanus' angle maximization problem Tangent half-angle substitution Trigonometric integral Trigonometric substitution Applications Fourier transform Wave equation

Other areas of mathematics

For examples of trigonometric functions as generating functions in combinatorics, see Alternating permutation. Dirichlet kernel Euler's formula Exact trigonometric values Exponential sum Trigonometric integral Trigonometric polynomial Trigonometric series

Geometric foundations

Altern base Angle Plane angle Solid angle Spherical angle Right angle Angle excess Angular distance Angular unit Degree (angle) Gon (angle) ( Grad, Gradian) Radian Turn (angle) Brocard points Chord (geometry) Circle (also see List of circle topics) Unit circle Hypotenuse Opposites post (pi) Ptolemy's theorem Pythagorean theorem Regiomontanus' angle maximization problem Thales' theorem Trigonometric function Trigonometry of a tetrahedron Triangle (also see List of triangle topics)

Trigonometric functions

Sine, Cosine, Tangent (trigonometric function), Cotangent, Secant (trigonometric function), Cosecant – see Trigonometric function atan2 cis—see Euler's formula Cofunction Exsecant Gudermannian function Inverse trigonometric functions Jyā, koti-jyā and utkrama-jyā Versine

Trigonometric identities

Trigonometric identity (list) De Moivre's formula Euler's formula Hermite's cotangent identity Lagrange's trigonometric identities Morrie's law Proofs of trigonometric identities Pythagorean trigonometric identity Tangent half-angle formula

Solution of triangles

Solution of triangles Law of sines Law of cosines Law of tangents Law of cotangents Mollweide's formula

More advanced trigonometric concepts and methods

Chebyshev polynomials Conway triangle notation Exact trigonometric constants Generalized trigonometry Gudermannian function Lissajous curve Polar sine Rational trigonometry Spread polynomials

Numerical mathematics

Abbe error Hypot Prosthaphaeresis Trigonometric interpolation Kunstweg, an algorithm for computing sines, introduced in the late 1500s

Trigonometric tables

Trigonometric tables Generating trigonometric tables Āryabhaṭa's sine table Bhaskara I's sine approximation formula Madhava's sine table Ptolemy's table of chords, written in the second century A.D. Rule of marteloio Canon Sinuum, listing sines at increments of two arcseconds, published in the late 1500s

Spherical trigonometry

Spherical trigonometry Half-side formula Haversine formula

Mnemonics

mnemonics in trigonometry All Students Take Calculus

Lists

List of integrals of trigonometric functions List of integrals of inverse trigonometric functions List of trigonometric identities Table of mathematical symbols

Outline of trigonometry

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