In this paper, we obtain finite series expansions for positive integer powers of sine and cosine functions. The terms of the expansions consist of trigonometric functions of multiple angles. Such formulas do exist in the literature. However, more than the final results themselves, we are ...
Contrary to the assertion in a recent paper that the formula for the tangent function of multiple angles is not widely known, whereas the corresponding ones for the sine and the cosine functions are common knowledge, it is pointed out that an entirely equivalent expression to one given in this...
Contrary to the assertion in a recent paper that the formula for the tangent function of multiple angles is not widely known, whereas the corresponding ones for the sine and the cosine functions are common knowledge, it is pointed out that an entirely equivalent expression to one given in this...
which are periodic but nonsinusoidal with respect to the time variation in the so-called deformant state, are collected from the power line system and processed in suitable operational amplifiers, operating as integrators, in such a way as to yield the sine and cosine harmonics of those waveforms...
Contrary to the assertion in a recent paper that the formula for the tangent function of multiple angles is not widely known, whereas the corresponding ones for the sine and the cosine functions are common knowledge, it is pointed out that an entirely equivalent expression to one given in this...
reactive power based on the first and second signals, and calibrating the calculated active and reactive powers with respect to the phase offset using first and second constants, in which the first and second constants respectively correspond to a sine value and a cosine value of the phase ...
reactive power based on the first and second signals, and calibrating the calculated active and reactive powers with respect to the phase offset using first and second constants, in which the first and second constants respectively correspond to a sine value and a cosine value of the phase ...
reactive power based on the first and second signals, and calibrating the calculated active and reactive powers with respect to the phase offset using first and second constants, in which the first and second constants respectively correspond to a sine value and a cosine value of the phase ...
COSINE functionINFINITE series (Mathematics)BINOMIAL coefficientsIn this paper, by means of the Fa脿 di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and ...
Three classes of improper integrals involving higher powers of arctanh, arctan, and arcsin are examined using the recursive approach. Numerous explicit formulae are established, which evaluate these integrals in terms of π, ln2, the Riemann zeta functio