I googled my problem and seemed to find the below solution. Do you think this would work?
"Question: I am remodeling a bathroom. The existing drain pipe is 1 1/2" copper tubing. What is the best way to connect a 1 1/2" PVC to 1 1/2" copper tubing?
Answer: I would take a 1 1/2" female copper adapter and solder it on the copper pipe. Then I would glue on a 1 1/2" PVC male adapter on the PVC. Connect the two with a compression fitting and you'll have a solid connection."
Do you think that is the way to go?