Question

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

Answer 1

\[F(x)=e^{Sin \frac{ X }{ 2 }}\]

Answer 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

Answer 3

Isn't it clearer to write pi + 2pi*k, where k is an integer?