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

Е. V. Velichko, I. G. Tkachenko


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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