$$F(x) = \sqrt{\sin x + \cos x}$$ I graphed this function and it seemed to be periodic but my textbook says that it's not. Is any other rule it's breaking...?
2026-04-01 08:20:19.1775031619
Can this be a periodic function
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Your function is periodic with period $2\pi$. Indeed, $\sin x$ and $\cos x$ are both periodic with period $2\pi$. (Technically, this only shows that $F(x)$ is either constant or periodic with period $2\pi/n$ for some $n$, but in this case the period is exactly $2\pi$.)