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Where the periodic function assumes its extreme values ​​and that these values ​​are?

Calculus1
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\[F(x)=e^{Sin \frac{ X }{ 2 }}\]
The function will have its peaks when sinx = 1 or -1. Using a unit circle, you can see that they occur at pi/2 + pix. But since the quantity is halved, you double this number and get: pi + 2pix
Isn't it clearer to write pi + 2pi*k, where k is an integer?

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