On the correctness of the determination of trigonometric functions by the system of functional equations

The article shows that the system of the functional equations$S(x+y)=S(x)C(y)+S(y)C(x),,C(x+y)=C(x)C(y)-S(y)S(x)$ defines abroader class of the functions than the trigonometric equations. Theconditions, which must be added to this system to obtain the uniquesolution have been developed $S(x)=sin{ax}...

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Bibliographic Details
Published inKarpats'kì matematinì publìkacìï Vol. 3; no. 1; pp. 15 - 21
Main Authors Е. V. Velichko, I. G. Tkachenko
Format Journal Article
LanguageEnglish
Published Vasyl Stefanyk Precarpathian National University 01.06.2011
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Summary:The article shows that the system of the functional equations$S(x+y)=S(x)C(y)+S(y)C(x),,C(x+y)=C(x)C(y)-S(y)S(x)$ defines abroader class of the functions than the trigonometric equations. Theconditions, which must be added to this system to obtain the uniquesolution have been developed $S(x)=sin{ax},,C(x)=cos{ax}$. Themethod of the reduction of the functional equations to thedifferential equations is used.
ISSN:2075-9827