The most important thing is to install the first piece at the same angle you are cutting the coped piece to, not what it says in the book. (What book?)
I make a mock up 90deg. joint, backnailed and glued about 10" long in each direction. I hold this up to the ceiling at each corner, and pencil along the bottom where it lands on to the wall. Remember, a lot of times, the mud will slope down in a corner, throwing off your measurement. The mock up jig shows it pretty much how it will end up. May be less, may be more than the actual number you are using.
A sloppy drywall mud job will frustrate you needlessly. The room could be perfectly 90 degrees, except six or eight inches from each corner. This also answers the question, "why cope?"
Use the mock up for up and down marks, u can't go wrong. A chalk line on the wall between the mock up points will also help you line up scarfs on long runs. Chalk the line 1/8" higher, cover it up with the crown.
The most important thing is how it looks, not how the numbers work. If the numbers don't work but it looks good, go with it. You will have plenty of time in retirement to ponder the why or why not of it.