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Find the minimum period of the following function : $f(x) = 3\sin(3x) + 2\cos^{2}(x)$

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    http://math.stackexchange.com/questions/873723/how-to-find-the-period-of-the-sum-of-two-trigonometric-functions – 2017-02-27
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    Do you have a generality for this form ? – 2017-02-27
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    Informal approach: Use a graphing utility – 2017-02-27
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    So hard to creat its graph . – 2017-02-27
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    You can easily create the graph on-line at [Desmos](https://www.desmos.com/). Aside from looking at the graph, you can use trigonometric identities to put the function into a form where the period is obvious. – 2017-02-27

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Use this fact $$\\\sin^{2k+1}(ax+b) \to T=\dfrac{2\pi}{|a|}\ \\\cos^{2k+1}(ax+b) \to T=\dfrac{2\pi}{|a|}\\$$ $$f(x) = 3sin3x + 2cos^{2}x\\ f(x) = 3sin3x + 2\frac{1+cos 2x}{2}=\\3sin 3x+1+cos 2x\\\to\begin{cases}sin 3x& T_1=\frac{2\pi}{3}\\cos 2x & T_2=\frac{2\pi}{2}\end{cases}$$now find l.c.m for $T_1,T_2$ $$T=\dfrac{\pi}{3}[2,3]=\dfrac{\pi}{3}\times 6=2\pi$$