The University of Miami board of trustees voted unanimously yesterday to accept an invitation to become the Big East Conference's 10th member, assuring the survival of one of the country's premier basketball conferences.

Miami will begin playing for all conference championships except baseball during the 1991-92 season and will have full voting privileges immediately. Miami's baseball team, a national powerhouse, will continue to play as an independent.

"We have become friends; we have become partners," university president Edward T. Foote II said at a news conference in Coral Gables, Fla. ". . . They are people whose values we share. They are our kind of people, by playing by the rules and having an obligation to our student-athletes to do it right" academically.

Big East Commissioner Mike Tranghese has stressed for the past month that adding Miami might be the only way to keep its three major football schools -- Syracuse, Pittsburgh and Boston College. He emphasized it again yesterday: "To be blunt with you, our future was at stake. I'm not certain we had {another} answer that would have satisfied the football concerns" of those three schools.

Miami will remain a football independent until the Big East reaches a grouping with other major college football teams. Tranghese said the other six Big East members will not share in football revenues and the four major college football schools will determine revenue-sharing among themselves.

Syracuse and Pitt had been mentioned in a number of scenarios in the expansion and realignment talks that reached a climax this summer. Sources said that a study by consultants for the Big Ten Conference listed Syracuse and Pitt, in that order, as the most desirable possibilities for expansion to a 12th team.

Expansion and realignment talks are expected to slow now that the four major football playing independents have chosen their futures -- Penn State joined the Big Ten, Florida State joined the Atlantic Coast Conference and Notre Dame withdrew from the College Football Association's television package with ABC and signed a five-year, $35 million deal with NBC.

"We've stopped {expanding}," Tranghese said. "The ACC said it's stopped. I don't think the Southeastern Conference {which has added South Carolina and Arkansas} is planning to add any more teams in the immediate future. The Pac-10 has said it won't expand and the Big Ten has a three-year moratorium on expansion."

The next major step is expected to be what Miami and its three Big East Division I-A partners can accomplish in reaching a football alliance, and Miami Athletic Director Sam Jankovich said there is no rush to decide.

The CFA's new deal with ABC-TV begins next season and won't expire until 1996 unless it is voided as a violation of antitrust laws, as the Federal Trade Commission has charged.

Tranghese said the Big East actually has three directions it can go. It prefers a football alliance with the ACC, a grouping that could result in two automatic bids to major bowls, including the Orange. Another possibility is an alliance with the Southwest Conference, which also would be an atttractive TV deal. The third possibility is adding football-playing independents without increasing its number of basketball members.

Tranghese said Virginia Tech would be one of those schools if the ACC and SWC alliances fail to emerge and the Metro Conference breaks up as a basketball conference. Already two of its football-playing schools, South Carolina and Florida State, have departed, and there are discussions going on that would bring Metro members Louisville, Cincinnati and Memphis State into a midwestern basketball conference with De Paul, Marquette, Dayton and possibly St. Louis.

The current plans for that conference do not include Metro members Virginia Tech, Tulane and Southern Mississippi, all of which play Division I-A football. The basketball-only Atlantic 10 Conference, which lost Penn State, also is expected to consider Virginia Tech.