Unique characteristics of trigonometric graphs

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If I was given a graph and told to prove that the function which was being plotted on the graph was trigonometric, how can I prove that? Are there any characteristics unique to trigonometric graphs which enable them to be differentiated from graphs of other functions?

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"Trigonometric"? What do you mean by that? Fourier showed us that every function can be written as the weighted sum of sines and cosines.

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Quiz:

On this plot, one of the curves is a trigonometric function and the other is not.

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How many of the functions below are made of trigonometric functions (in a closed-form expression) ?

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