As a senior in 1973, he helped the Lancers reach the finals of the Central Coast Section playoffs, before losing the title game 32–30 to Saratoga High School.However, feeling that the quarterback position was in excellent shape with Roger Staubach, Danny White and Glenn Carano, the Cowboys needing a tight end to join Billy Joe DuPree, deviated from their philosophy and chose Cosbie instead.In his first 2 seasons, he was a backup behind DuPree and Jay Saldi, playing mainly on special teams and as a blocking tight end on short-yardage and goal-line situations.In 1981, he almost won the starting tight end spot, but was still able to share it with Dupree and tied for the team lead with 5 touchdown receptions.He is part of the Cowboys franchise's legacy of great tight ends that includes: Jim Doran, Lee Folkins, Pettis Norman, Mike Ditka, Billy Joe DuPree, Jay Novacek and Jason Witten.He is also co-owner of the La Jolla Group, along with fellow Santa Clara University athletes, Kurt Rambis and Rich Brown.