Convencer vs. persuadir

The Spanish words 'convencer' and 'persuadir' both translate to 'to convince' or 'to persuade' in English, but they have subtle differences in usage and connotation.

Convencer

'Convencer' means to make someone believe or be sure about something based on the presentation of logical arguments or evidence. It involves appealing to reason and rationality.
Logré convencer a mi jefe de que la reunión era necesaria.
(I managed to convince my boss that the meeting was necessary.)
Tuve que presentar muchos datos para convencer al comité de aceptar mi propuesta.
(I had to present a lot of data to convince the committee to accept my proposal.)
Él no estaba seguro al principio, pero después de ver los números, lo convencí.
(He wasn't sure at first, but after seeing the numbers, I convinced him.)

Persuadir

'Persuadir' means to influence someone's decision or behavior through reasoning or emotional appeal, often involving more subjective or motivational elements. It can appeal both to logic and emotions.
Traté de persuadir a mis amigos para hacer un viaje a la playa este fin de semana.
(I tried to persuade my friends to take a trip to the beach this weekend.)
Ella usó su carisma para persuadir al jurado a favor de su cliente.
(She used her charisma to persuade the jury in favor of her client.)
A pesar de las dudas iniciales, su discurso persuasivo hizo cambiar la opinión del público.
(Despite initial doubts, his persuasive speech changed the audience's opinion.)

Summary

While both 'convencer' and 'persuadir' are used to talk about influencing others, 'convencer' focuses more on logical arguments and evidence, while 'persuadir' may involve emotional appeal and subjective factors as well as logical reasoning.