Synonyms for Determine (same or very similar meaning)
WordNet sense 1 (decide upon or fix definitely):
fix, limit, set, specify
WordNet sense 2 (find out, learn, or determine with certainty, usually by making an inquiry or other effort):
ascertain, check, learn, see, watch, find out
WordNet sense 3 (establish after a calculation, investigation, experiment, survey, or study):
find
WordNet sense 4 (settle conclusively; come to terms):
settle, square up, square off
WordNet sense 5 (shape or influence; give direction to):
influence, mold, regulate, shape, shape
WordNet sense 6 (reach, make, or come to a decision about something):
decide, make up one's mind
From the ODE community, based on WordNet
add/edit