Years ago, there were two calculators--the TI-82 and TI-85.
The TI-82 was the lesser of the two. It evolved into the TI-83, TI-83 Plus, and more recently the TI-84 series (plus, silver, etc).
The TI-85 was a more advanced calculator with more advanced functions. It was eventually replaced by the TI-86.
These have always been two seperate calculators. The TI-84 is essentially a TI-83 Plus in a new case with more RAM and a few new features. The TI-86 is a higher powered machine that will always do more than a TI-84 no matter how plus or silver you can get it.
So the answer to your question is...no. You want a TI-86 (or a used TI-85).
Plane trig sounds to me like it will need more than a TI-84 will provide, but don't take my word for that (I've never taken plane trig and probably never will).