How to cut an arched board for bookshelf?

I am finishing up a built-in entertainment center in my living room. The only thing I'm having trouble with is how to make an arched board that faces the top of the shelf. The arch needs to be about 39.5 inches wide and about 4 inches high so that I can cut it into a 1x6. How can I draw a symmetrical template without a wide-format printer? Since it is oblong I can't use a string and pencil. Any ideas?