" I have been doing this new shaping workout for the past few months and have yet to see any progress."
My question is in regards with the last part of the sentence " have yet to see any progress" what does that mean? what's the use "yet" in this particular sentence?
It would make more sense to me if it were "I've not seen any progress yet"
Both sound fine to me and have the same meaning, although the "have yet" construction seems a little more formal and stuffy to me. By the way, "I've not seen any progress yet." is not something you'll hear in the United States, at least. It might be a British construction. In the US, people would say "I haven't seen any progress yet," or they would drop the contraction altogether to sound more formal.
I think this may have something to do with a sort of sense of feeling or emotion. Personally I would say "I haven't seen any progress yet" if it was just a sort of casual observation about the current situation and that progress would be expected shortly.
"I've yet to see any progress!" indicates a bit of a feeling of frustration, and that maybe the whole effort may be a bit of a waste of time and that you're considering giving it up. Either dissing it altogether or just putting it on the back burner.