Let's assume that we've tossed a fair coin five times already and that all were heads. This answer just reflects my experiences with the various precalc textbooks I've seen.That's a very interesting question. Different teachers teach different things. (Keep in mind this is all largely dependent on what is actually taught in the specific courses you're going to take. So this is something to consider when deciding if you want a primer in the trig before jumping into precalc. It's a hard class for many students and moves quickly.
Just keep in mind that precalc (usually) covers *a lot* of material. On the other hand, if you feel okay about learning trigonometry in a quicker manner, precalc should give you everything you need on this front.
If you aren't sure you can check out some trigonometry stuff on Khan Academy and get a feel for where you're at. If you think that trig will be a difficult topic given your current background, you could benefit from a trig class because it will move through the topics more slowly. I think this largely depends on your current comfort level with mathematics. is it more likely that I will struggle in calc without taking trigonometry on top of pre-calc? The Precalc course that I taught at my university contained all of the trig that was in our Trig course, but it was introduced at a faster pace in the precalc course, because precalc has much more topics in addition to trig. It likely depends on the pre-calc course, but the ones that I have seen cover all the trig you will need to be successful in calculus.
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