[1] Born in Palermo, Kingdom of the Two Sicilies; at the age of 12 years, Trentacoste began apprenticing with the sculptor Domenico Costantino.
As a young man he travelled through Italy, including Naples, and spent some years in Florence starting in 1878.
The commission of a triumphal arch made for the visit of King Umberto I garnered Trentacoste enough money to move to Paris in 1880, where he met with the sculptor Giovanni Antonio Lanzirotti.
His Pia de' Tolomei was bought by the English painter Edwin Long, who had introduced him to buyers in London.
Among his pupils were Torello Santini, Bruno Catarzi, Mario Moschi, Marino Marini, Paolo Abbate, and Giuseppe De Angelis.