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I've been studing the periodic functions and i was just wondering how to calculate the fundamental period for functions like : |sin(x)|+ |cos(x)|

Which the value of LCM is a period of function but not fundamental period , So i was just looking for a way to predict it without ploting it and also it seems in these types of functions fundamental period is half of value of LCM , is it correct ?

Elias
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    Wouldn't you expect any describable process to give the same period to $|\sin x| + |\cos x|$ and to $|\sin(x+\pi/2)| - |\cos(x)|$? You might want to graph that last one... – Eric Towers Mar 16 '21 at 09:13
  • Nice ! it becomes zero and there is no fundamental period ... but there is a trigonometric approach to this because $|\sin(x+\pi/2)| = |\cos(x)|$ but what about the function which i asked ? – Elias Mar 16 '21 at 09:55
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    Does this answer your question? https://math.stackexchange.com/questions/164221/period-of-the-sum-product-of-two-functions#:~:text=If%20you%20are%20suppose%20to,LCM(a%2Cb). – Koro Mar 16 '21 at 10:18

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