This is the 2811th most frequent French word.
convaincus
"Convaincus" means "convinced" in English.
In this sentence, 'convaincus' is used as an adjective agreeing in gender and number with the subject (nous) to express certainty or firm belief.
Nous sommes convaincus que cet effort portera ses fruits.
We are convinced that this effort will bear fruit.
Here, 'convaincus' is used as an adjective modifying the plural subject (les élèves) to indicate their acceptance or agreement with the explanation.
Les élèves semblaient convaincus par l'explication du professeur.
The students seemed convinced by the teacher's explanation.
In this context, 'convaincus' describes the state of being persuaded, matching the gender and number of the addressed subject (vous).