Answer
$T=2\pi$
Work Step by Step
For a function of the form $\sin{(ax+b)}+c$, the period $(T)$ is given by:
$$T=\dfrac{2\pi}{a}$$
For $\sin{\left(x-\dfrac{\pi}{4}\right)}+1$, $a=1$
$T=\dfrac{2\pi}{1} = 2\pi$
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