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# trigonometric function

1. Also called circular function. a function of an angle, as sine or cosine, expressed as the ratio of the sides of a right triangle.
2. any function involving only trigonometric functions and constants.
3. the generalization of these to functions of real or complex numbers. Also called trig function (for defs. 1, 2).
[1905-10]

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In mathematics, one of six functions (sine, cosine, tangent, cotangent, secant, and cosecant) that represent ratios of sides of right triangles.

They are also known as the circular functions, since their values can be defined as ratios of the x and y coordinates (see coordinate system) of points on a circle of radius 1 that correspond to angles in standard positions. Such values have been tabulated and programmed into scientific calculators and computers. This allows trigonometry to be easily applied to surveying, engineering, and navigation problems in which one of a right triangle's acute angles and the length of a side are known and the lengths of the other sides are to be found. The fundamental trigonometric identity is sin2θ + cos2θ = 1, in which θ is an angle. Certain intrinsic qualities of the trigonometric functions make them useful in mathematical analysis. In particular, their derivatives form patterns useful for solving differential equations.

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Universalium. 2010.

### Look at other dictionaries:

• trigonometric function — n. any of the basic functions (as sine, cosine, tangent, etc.) of an angle or arc, usually expressed as the ratio of pairs of sides of a right triangle: see SINE1 …   English World dictionary

• trigonometric function — noun Date: 1909 1. a function (as the sine, cosine, tangent, cotangent, secant, or cosecant) of an arc or angle most simply expressed in terms of the ratios of pairs of sides of a right angled triangle called also circular function 2. the inverse …   New Collegiate Dictionary

• trigonometric function — noun function of an angle expressed as a ratio of the length of the sides of right angled triangle containing the angle • Syn: ↑circular function • Hypernyms: ↑function, ↑mathematical function, ↑single valued function, ↑map, ↑mapping …   Useful english dictionary

• trigonometric function — trig′onomet′ric func′tion n. math. a function of an angle, as the sine or cosine, expressed as the ratio of the sides of a right triangle Also called circular function Etymology: 1905–10 …   From formal English to slang

• trigonometric function — noun Any function of an angle expressed as the ratio of two of the sides of a right triangle that has that angle, or various other functions that subtract 1 from this value or subtract this value from 1 (such as the versed sine) See Also:… …   Wiktionary

• inverse trigonometric function — noun A function that is the inverse of an appropriate restriction of a trigonometric function …   Wiktionary

• logarithmic trigonometric function — noun The logarithm of a trigonometric function …   Wiktionary

• inverse trigonometric function — noun : the inverse of any of the six trigonometric functions …   Useful english dictionary

• Trigonometric — Trig o*no*met ric, Trigonometrical Trig o*no*met ric*al, [Cf. F. trigonom[ e]trique.] Of or pertaining to trigonometry; performed by the rules of trigonometry. [1913 Webster] {Trig o*no*met ric*al*ly}, adv. [1913 Webster] {Trigonometrical curve} …   The Collaborative International Dictionary of English

• Trigonometric functions — Cosine redirects here. For the similarity measure, see Cosine similarity. Trigonometry History Usage Functions Generalized Inverse functions …   Wikipedia