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Is the function $\frac{\sqrt{\sin(x)}}{\cos(x)}$ periodic? If that is the case, what are the steps to calculate the period?

rik
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  • It is clearly periodic, since $f(x+2\pi)=f(x)$. – HappyDay Feb 27 '23 at 20:30
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    Why do you say it is not elementary? It looks like an elementary function to me. But what are you expecting its domain to be. As a function of a real variable it is not defined when $\sin(x)$ is negative. If you want to be a function of a complex variable, then you need to explain where you are putting the branch cut in $\sqrt{\cdot}$. – Rob Arthan Feb 27 '23 at 20:37
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    The function is not defined for $(\pi+2k\pi,2\pi+2k\pi), k \in \Bbb Z$. For the domain of definition the function is periodic where it seems to resemble the tangent. – WindSoul Feb 27 '23 at 21:10
  • @RobArthan You are right, the function is elementary. I was a bit confused about the definition of "elementary function". I expect its domain to be a subset of real numbers, specifically the domain that WindSoul mentioned : $(2k\pi,\pi+2k\pi), k \in \mathbb{Z}$ – rik Feb 28 '23 at 11:19

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