This randomized phase II trial studies the side effects and how well modestly reduced-dose intensity-modulated radiation therapy (IMRT) with or without cisplatin works in treating patients with oropharyngeal cancer that has spread to other places in the body (advanced). Radiation therapy uses high energy x rays to kill tumor cells. Drugs used in chemotherapy, such as cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. It is not yet known whether IMRT is more effective with or without cisplatin in treating patients with oropharyngeal cancer.