360 degrees is a circle not a line. Line of sight is looking at you plus their perhriphial vision, you can see them, they are not "looking" if you are not in their line of sight(outside of their cone of sight i.e. direct line plus perhriphial) the passive perception comes into play.
Again, there is no facing in 5E so therefore no "field" (cone plus peripheral) of sight. A creature can establish Line of Sight all around them. Maybe this will help:
A sentry is standing in a clearing (why? no clue... not important) in Bright Light. Rogue A, B, and C all have Heavy Obscurment in very thick woods. Each is trying to move from their position across an opening to other Heavy Obscurement. There is no facing in 5E, so the sentry has Line of Sight on A (white line), B (yellow line), and C (red line).
From your PoV, he will see A,
maybe B depending on how good his peripheral vision is, but not C because he is "behind the sentry". While I agree with you that is how it
should work and would if 5E used facing, it doesn't. So, he will see all three.
Now, ToM, the DM can simply tell the player of Rogue C, "He is looking away from your position" and deny Line of Sight I suppose. But he could just as easily say the sentry is occasionally turning to look behind himself so might see Rogue C.