Sentence examples for use of trigonometric representations from inspiring English sources

In [2], de Vicente, Gandy, Sanchez-Ruiz presented a novel approach to the evaluation of the information entropy of Gegenbauer polynomials, which makes use of trigonometric representations for these polynomials and complex integration techniques.

Viète showed that the solution of many algebraic equations could be expressed by the use of trigonometric expressions.

The use of trigonometric functions to express components is introduced next, and the roots of unity are discovered by surprisingly laborious means.

Afterwards, the system is analytically solved with the use of trigonometric series.

It is worthy to note here that the two linearization formulas (17) and (18) of Chebyshev polynomials can also be obtained from their trigonometric representations.

In the second application, we give some new trigonometric identities by transporting the linearization formulas to their trigonometric representations.

"Often, the art is very rooted in math – computers make great use of randomness, trigonometric functions, and geometry.

These 3D-chiral quadratic indices make use of a trigonometric 3D-chirality correction factor.

Shapley could not make use of the trigonometric parallax method, since there are no variables close enough for direct distance measurement.

And what that results in, when you look at the trigonometric form of the Fourier series, is that in fact, those conditions, if you put the terms all together, lead you to a trigonometric representation, which involves only sine terms in other words, no cosine terms.

In the following, we give a trigonometric representation for equation (35).