The Vatican Council (opened on 8 December, 1869) defined as "a divinely revealed dogma" that "the Roman Pontiff, when he speaks ex cathedra — that is, when in the exercise of his office as pastor and teacher of all Christians he defines, by virtue of his supreme Apostolic authority, a doctrine of faith or morals to be held by the whole Church — is, by reason of the Divine assistance promised to him in blessed Peter, possessed of that infallibility with which the Divine Redeemer wished His Church to be endowed in defining doctrines of faith and morals; and consequently that such definitions of the Roman Pontiff are irreformable of their own nature (ex sese) and not by reason of the Church's consent"1 - Source: Explanation of papal infallibility | Infallibility | New Advent.
1. cf. Denzinger 1839 And so We, adhering faithfully to the tradition received from the beginning of the Christian faith, to the glory of God, our Savior, the elevation of the Catholic religion and the salvation of Christian peoples, with the approbation of the sacred Council, teach and explain that the dogma has been divinely revealed: that the Roman Pontiff, when he speaks ex cathedra, that is, when carrying out the duty of the pastor and teacher of all Christians by virtue of his supreme apostolic authority he defines a doctrine of faith or morals to be held by the universal Church, through the divine assistance promised him in blessed Peter, operates with that infallibility with which the divine Redeemer wished that His church be instructed in defining doctrine on faith and morals; and so such definitions of the Roman Pontiff from himself, but not from the consensus of the Church, are unalterable.
The question is, does the Pope teach infallibly ONLY when he speaks ex cathedra? Are there instances when a Pope has taught infallibly but not precisely as according to the definition by the Vatican Council? If so, what are some examples?