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.
When the Cowboys' turn came up in the third round, the highest rated player on their board was quarterback Joe Montana.
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.
[5] After being passed over by the next five teams in the draft order, the San Francisco 49ers selected Montana as the final player of the third round.
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.
[7] He decided to retire during training camp that season, after playing for 10 years in the NFL and also in three NFC Championship games.
He is also co-owner of the La Jolla Group, along with fellow Santa Clara University athletes, Kurt Rambis and Rich Brown.