This article pushes the role of sine and cosine functions beyond traditional purpose determining sides a right triangle, into realm lengths any triangle with practically same ease. Extended are formulated dependent on two angles (instead one) — sin*(α,γ) cos*(α,γ)—that allow (via direct application) computation shorter scalene as resul...

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRS...

In this paper, we provide a concise proof of Oppenheim’s double inequality relating to the cosine and sine functions. In passing, we survey this topic.

Abstract Metaheuristic algorithms based on intelligent rules have been successfully developed and applied to solve many optimization areas over the past few decades. The sine–cosine algorithm (SCA) imitates behaviour of transcendental functions while sine cosine are presented explore exploit search space. SCA starts by random population executes iterative evolution processes update standard evo...

A new motion estimation scheme, Discrete-Cosine/SineTransform Based Motion Estimation (DXT-ME) utilizing the principle of orthogonality of cosine and sine functions to estimate, in the transform domain, displacements from the motion information contained in the pseudo-phases of the images of moving objects, is proposed. The computational complexity of this method is only O ( N 2 ) + O d c t for...

In this note, using the multisection series method, we establish the formulas for various power sums of sine or cosine functions.

In this paper, four types of fractional Fourier cosine and sine Laplace weighted convolutions are defined, the corresponding convolution theorems associated with transform, transform derived in detail. Furthermore, relationship between (sine) existing studied, Young's type theorem is also investigated. addition, as an application for (sine)-Laplace convolution, system convolution-type integral ...

– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...

– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...