synes = think/feel as in opine; seem: "I think it's a good film." "It seems harmless."
tenker = think as in is engaged in the act of thinking: "I think, therefore I am."
tror = believe (both meanings), think: "I believe in God." "I believe that's the case." "I think so."
As you can see, there's quite some overlap. The most common mistake among English speakers, is using "tenker" when sharing opinions and doubts.