You should set your Illustrator canvas to be at 1920x1080 pixels if you are going to be outputting ONLY on your 48" LCD as final.
I believe you got your Illustrator canvas size of 2862 x 1587 by using the diagonal 48" multiplied by a 72 ppi resolution - doesn't work that way bub.
However, in the event that you might be using your artwork for print or anything else, I would recommend you to set it to a higher resolution that supports fine-printing, and also is in a 16:9 aspect ratio, and then output to a jpeg and downscale to 1920x1080 for display on your LCD. That would cover all bases.