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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and…

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Overview

Notation

Right-angled triangle definitions

Radians versus degrees

Unit-circle definitions

Algebraic values

Definitions in analysis

Basic identities

Inverse functions

Applications

History

Etymology

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Trigonometric functions

Nodes216
Edges215
Triples119
Avg. degree1.99
Density0.009259
Components1

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Trigonometric functions

Top relations

related to history · 38
Trigonometric functions → Al-Khwārizmī, All, Arabic, Aryabhatiya, Battānī, BCE, Bhāskara II, CE, Circa, Din, Gupta, Habash, Harrānī, Hasib, Hipparchus, Indian, Islamic, Jamshīd, Jābir, Kāshī
related to External links · 9
Trigonometric functions → EMS Press, Encyclopedia, Eric, Mathematics, MathWorld, Tangent, Trigonometric, Visionlearning Module, Wave MathematicsGonioLab Visualization
related to Basic identities · 8
Trigonometric functions → Euler's, For, List, Many, One, Proofs, These, This
related to Radians versus degrees · 8
Trigonometric functions → For, However, In, It, Moreover, One, The, Thus
related to Definition via integration · 6
Trigonometric functions → Also, Another, For, Karl Weierstrass, On, Thus
related to Power series expansion · 6
Trigonometric functions → Maclaurin, Taylor, Term-by-term, The, Therefore, These
related to Definitions in analysis · 5
Trigonometric functions → Course, Hardy, Pure Mathematics, Thus, Various
related to Inverse functions · 5
Trigonometric functions → As, However, The, To, When
related to Right-angled triangle definitions · 5
Trigonometric functions → If, In, This, Thus, Various
related to Unit-circle definitions · 5
Trigonometric functions → Euclidean, Let, The, This, While

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Important terminology

displaystyle functions sin trigonometric cos sine cosine pi angle function frac tan cot used also real right angles tangent begin

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
sound or light waves.Under rather general conditionsinstance ofThe characteristic wave patterns of periodic functions are useful for modeling recurring phenomena0.80text
a periodic function finstance ofThe characteristic wave patterns of periodic functions are useful for modeling recurring phenomena0.80text
Trigonometric functionsrelated to Angles and sides of a triangleIn0.60section
Trigonometric functionsrelated to Angles and sides of a triangleThey0.60section
Trigonometric functionsrelated to Basic identitiesMany0.60section
Trigonometric functionsrelated to Basic identitiesThis0.60section
Trigonometric functionsrelated to Basic identitiesList0.60section
Trigonometric functionsrelated to Basic identitiesThese0.60section
Trigonometric functionsrelated to Basic identitiesProofs0.60section
Trigonometric functionsrelated to Basic identitiesFor0.60section
Trigonometric functionsrelated to Basic identitiesEuler's0.60section
Trigonometric functionsrelated to Basic identitiesOne0.60section

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