We have to solve:
$ \sin(\dfrac{1}{2}x + \pi) $ = $\dfrac{1}{2}\sqrt{2}$
I get these answers:
$ x = -1\frac{1}{2}\pi + k2\pi\quad \lor\quad x =-\frac{1}{2}\pi + k2\pi$
Both these answers can be merged into this answer right?:
x = $\frac{1}{2}\pi + k\pi$
Also, are these 2 mergable (and have I merged them correctly or not?):
$ x = -\frac{1}{2}\pi+k6\pi\quad$ and $\quad x = 3\frac{1}{2}\pi+k6\pi$
=
$ x = 1\frac{1}{2}\pi+k3\pi$