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

Е. V. Velichko, I. G. Tkachenko

Abstract


The article shows that the system of the functional equations $S(x+y)=S(x)C(y)+S(y)C(x),\,C(x+y)=C(x)C(y)-S(y)S(x)$ denes a broader class of the functions than the trigonometric equations. The conditions, which must be added to this system to obtain the unique solution have been developed $S(x)=\sin{ax},\,C(x)=\cos{ax}$. The method of the reduction of the functional equations to the dierential equations is used.

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