trigonometric function

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Related to trigonometric function: exponential function, Inverse trigonometric function

trigonometric function

In a right triangle, the three main trigonometric functions are

sine θ = opposite / hypotenuse

cosine θ = adjacent / hypotenuse

tangent θ = opposite / adjacent.

trigonometric function

A function of an angle expressed as the ratio of two of the sides of a right triangle that contains that angle; the sine, cosine, tangent, cotangent, secant, or cosecant. Also called circular function.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

trigonometric function

1. (Mathematics) Also called: circular function any of a group of functions of an angle expressed as a ratio of two of the sides of a right-angled triangle containing the angle. The group includes sine, cosine, tangent, secant, cosecant, and cotangent

2. (Mathematics) any function containing only sines, cosines, etc, and constants

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

trig′onomet′ric func′tion

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.

[1905–10]

trigonometric function

In a right triangle, the trigonometric functions are: sine θ = ^opposite/_hypothenuse cosine θ = ^adjacent/_hypothenuse tangent θ = ^opposite/_adjacent

trig·o·no·met·ric function

(trĭg′ə-nə-mĕt′rĭk)

A function of an angle, as the sine, cosine, or tangent, whose value is expressed as a ratio of two of the sides of the right triangle that contains the angle.

The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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Noun

trigonometric function - function of an angle expressed as a ratio of the length of the sides of right-angled triangle containing the angle

circular function

function, mapping, mathematical function, single-valued function, map - (mathematics) a mathematical relation such that each element of a given set (the domain of the function) is associated with an element of another set (the range of the function)

sine, sin - ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle

arc sine, arcsin, arcsine, inverse sine - the inverse function of the sine; the angle that has a sine equal to a given number

cos, cosine - ratio of the adjacent side to the hypotenuse of a right-angled triangle

arc cosine, arccos, arccosine, inverse cosine - the inverse function of the cosine; the angle that has a cosine equal to a given number

tangent, tan - ratio of the opposite to the adjacent side of a right-angled triangle

arc tangent, arctan, arctangent, inverse tangent - the inverse function of the tangent; the angle that has a tangent equal to a given number

cotan, cotangent - ratio of the adjacent to the opposite side of a right-angled triangle

arc cotangent, arccotangent, inverse cotangent - the inverse function of the cotangent; the angle that has a cotangent equal to a given number

sec, secant - ratio of the hypotenuse to the adjacent side of a right-angled triangle

arc secant, arcsec, arcsecant, inverse secant - the inverse function of the secant; the angle that has a secant equal to a given number

cosec, cosecant - ratio of the hypotenuse to the opposite side of a right-angled triangle

arc cosecant, arccosecant, inverse cosecant - the angle that has a cosecant equal to a given number

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Based on the derivation above, the angle calculation problem is transformed to root finding problem for polynomial, as there will be no trigonometric function of Snell's law.

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When [mu][lambda] > 0, the trigonometric function solution corresponding to the parameter values in Case 1 can be written as

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which results in the following formula in terms of generalized trigonometric function defined in [26]

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When I was studying Chemical Engineering at the University of Pennsylvania, I struggled with all the homework and lab work; not with the technical challenge but with the amount of time required to actually do the labor-intensive table look-ups for each trigonometric function used.

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When [e.sub.2] = 1, [e.sub.1] < 0, [e.sub.0] = 0, the following trigonometric function solution can be obtained:

The Jacobi Elliptic equation method for solving fractional partial differential equations

On the basis of the Ritz method, [[xi].sub.j](x) can be approximately expressed as a known trigonometric function sin [[alpha].sub.j]x for the antisymmetric mode or cos [[beta].sub.j]x for the symmetric mode, in which [[alpha].sub.j], [[beta].sub.j] are the known constants.

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In this paper, monotonicity of data is retained by developing constraints on free parameters in the specification of rational trigonometric function and bicubic blended function.

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We claim that the tanh method can be extended by replacing tanh function with some generalized functions f(x), such as polynomial function, trigonometric function and Jacobi elliptical function.