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The Proof of the Non-periodicity of Four Kinds of Compound Trigonometric Functions

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DOI: 10.25236/emcs.2018.104


Wusheng Wang, Caihong Chen, Yubo Wang

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Wusheng Wang


The non-periodicity of the function is an important part of the field of mathematics. First of all, this paper sums up a method to prove that the is a non-periodic function starting from the periodic definition, through the thought of the classified discussion, using the knowledge that the rational number is not equal to the irrational number in the real number, and the existing theorem conclusions. Secondly, another method of proving the non-periodic of function is obtained, based on ideas of number form combining, through the theorem that the limiting value of the adjacent intersections of graphics with the x axis is 0. Finally, with ideas of analogical proof method, the conclusion that and are non-periodic functions are proved.


Non-periodic Function, Classification and Discussion, Combination of Number and Shape, Function Limit, Compound Trigonometric Function