 Cook has no direct descendants—all of his children died before having children of their own.Cook's first posting was with , serving as able seaman and master's mate under Captain Joseph Hamar for his first year aboard, and Captain Hugh Palliser thereafter.In October and November 1755, he took part in "Eagle"'s capture of one French warship and the sinking of another, following which he was promoted to boatswain in addition to his other duties.