In his sophomore year, he averaged 15.1 points and 12.6 rebounds per game, leading BYU to the 1971 WAC Championship.

In his junior year, he again led his team to the WAC Championship, averaging 22.3 points and 12.8 rebounds per game, and being awarded All-American Honors by the United Press International, making him the first non-American player to achieve that.

In the 1972 NBA draft, he was picked by the Portland Trail Blazers, in the 10th round (144th overall), but he opted to stay with BYU.

As a senior, he averaged 20.2 points and 9.5 rebounds per game, and again was given All-American Honors, by the United Press International.

[5] At the 1973 NBA draft, Ćosić was picked by the Los Angeles Lakers, in the 5th round (84th overall).

[6] He rejected several professional offers from the NBA and ABA, and returned home to Croatia, where he again played with KK Zadar, from 1973 to 1976.

In total, Ćosić played in four Summer Olympic Games: 1968, 1972, 1976, and 1980 in Moscow, when he led his team as captain to the gold medal.

Following his playing days, Ćosić returned to coaching, and he led the senior Yugoslav national team to a silver medal at the 1988 Summer Olympics in Seoul, and two bronze medals at the 1986 FIBA World Championship, and the 1987 EuroBasket.

He also recognized a young talent in Dejan Bodiroga, whom he helped set off his career.

Ćosić turned down coaching offers so that he could help Croatia during war-time in the early 1990s.

[12] During his time at Brigham Young University, Ćosić converted to the Church of Jesus Christ of Latter-day Saints, and he later served as the presiding priesthood holder in post-communist Croatia.

His daughter, Ana, published his writings in May 2019 in Croatian under the book name Play, Believe, Live.