Trapanese completed his bachelor's degree in Composition at the Manhattan School of Music, and later an M.A. in Music for Visual Media at UCLA, with support from the Henry Mancini fund. Joseph's tutors included Giampaolo Bracali, Bruce Broughton, Paul Chihara, Roger Bourland, Jack Smalley, and Martin Bresnick, and he also engaged in brief studies with Louis Andriessen, Aaron Jay Kernis, Julia Wolfe, Mark Snow, and Ira Newborn. From 2008–2011, Trapanese taught the Electronic Music and Composition curriculum at UCLA's Herb Alpert School of Music.