Outline of trigonometry explained

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) (aka 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

See also

• Algebra
• Hyperbolic function
• List of exponential topics
• Outline of geometry
• Precalculus
• Spherical geometry
• Table of mathematical symbols

External links

• An introduction to trigonometry
• Benjamin Banneker's Trigonometry Puzzle at Convergence
• Dave's short trig course
• Trigonometric Delights, by Eli Maor, Princeton University Press, 1998. Ebook version, in PDF format, full text presented.
• Trigonometry by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented.
• Trigonometry FAQ
• Trigonometry on Mathwords.com index of trigonometry entries on Mathwords.com
• Trigonometry on PlainMath.net Trigonometry Articles from PlainMath.Net