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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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    $\begingroup$ Are you sure that the question was phrased this way ? $\endgroup$
    – user65203
    Aug 24, 2018 at 6:32

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Quiz:

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

enter image description here

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

enter image description here

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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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  • $\begingroup$ Was that shown in the Fourier series? $\endgroup$
    – Robin Ting
    Aug 24, 2018 at 6:34
  • $\begingroup$ It works only on periodic functions, based on what I've read from wikipedia. Therefore, if one value of the function repeats itself at regular input intervals, It can be written as the weighted sum of sines and cosines. Is my conclusion correct? $\endgroup$
    – Robin Ting
    Aug 24, 2018 at 6:53

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