Answer
The graphs do not appear to coincide.
Work Step by Step
The graph of $y=\sin (x+ \pi )$ (the red graph) and $y=\sin x$ (the blue graph) do not coincide.
For $x=\frac{\pi }{2}$, we have$$\sin (\frac{\pi }{2}+\pi )=-1 \neq 1 = \sin \frac{\pi }{2}.$$
