Move an Image with the Player

NOOB ALERT

I'm not sure if it is possible (or if it's just really hard). In my game, the player is moved with WASD. When the player presses a or d, it rotates the player.

Now, what I want to is when the player rotates, the image will rotate to half the angle that the player rotated at. Now, the hard part is that eventually, I figured that the player would rotate to an angle where there would be no background showing, so I want to have each side of the image "connected". This means that the right end of the image is touching the left. If I don't make any sense, tell me. A video would be helpful, or you could show me some code, that would also be helpful.

Tell me if this is too hard or impossible

Thanks!