16th nissan (first day of the omer / 2nd day pesach) is same day of the week as shavuot.
note: in diaspora or israel, we count from the 16th, one can verify this because if we didn`t then shavuot would not come out on the right day (the 50th day, the day after the 49th day of the omer).
In diaspora, the 16th is chol hamoed. In israel, it is yom tov. But still, we count from the 16th.
there is a pasuk, as suggested by raul, that says you count the omer from the day after shabbat. oral tradition says we count from the first day of pesach, and I think relates it to that verse, saying shabbat here refers to pesach yom tov. It may be, as raul said, that first day pesach was shabbat at that time. (though I would say, perhaps that only refers to the first time).
If that is the case though that the 15th was Saturday.
Then the 16th was sunday, and shavuot was sunday.
I have found a few webpages that say that according to the gemara, the Torah was given on shabbat. So shavuot was on shabbat.
Shavuot is the "50th day". The same day of the week as the first day of the omer. (see kaluach software, for the pattern) 1st, 8th, 15th, +7, e.t.c. of the omer, up to "50th". Are same day of the week.
So the 16th nissan was saturday.
That makes the 15th, sunday.
So judging by the gemara, the other ideas, raul`s , that 16th was sunday, or Yaakov`s that 15th was thursday, seem wrong. Raul`s argument was just a suggestion based on a pasuk.
Yaakov, what is your source for saying the 15th was a thursday?
note- there are some variables here.. if the torah was given at night(I think it was given in the morning, but would have to check, rashi quotes some gemara there).. But another variable is the teaching that in those days, jewish days began in the morning not at night. So for example, when the tenach says "on the 14th, in the night" , and at another point says, on the 15th. It is saying the same thing. Because in those days, the 14th in the night, was the end of the 14th. And later, we started counting days from the night. So on the 15th/ night of the 15th, the start of the 15th.