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You have to have your math down if you want to do well in physica IMO. I took Physics for Engineers though, so that might be a little different.
I think Doc Henry is right in that you shouldn't go re-take a course in math. I would say the biggest thing you can do to help is to make sure you keep up when the class actually starts. Reviewing and re-learning bits and pieces of math isn't that bad as long as you keep up with the course's speed. Don't expect to pull an all-nighter and expect a good grade in physics since you aren't very confident about your grasp of mathmatics. Also, do lots of problems (even if you just quickly set up the solution without actually calculating and then checking with the answer book to see if you are on the right track). You are going to have to do problems till it's second nature to you if you don't already have your math down cold.
I've got you all beat - between my last math class (calculus for business majors) and physics I, 20 years passed. I tested out of college algebra, so I never took it. I used exactly ZERO college algebra/calculus in the intervening 20 years, and I did just fine in physics. No big deal!! Don't sweat it.
I think it might be a lot different. I took the "non-engineer physics," and the algebra and trig concepts seemed to be very basic. My physics class actually had a trig review to go along with Newtonian mechanics, and I would say that most people would have no problem picking it up with a good day or two of reviewing.
Trig shouldn't be necessary, but ultimately you may want to take it because you're going to have to take at least up to calculus 1 (sometimes 2 or 3) if you want to get into med school.
It depends on your school/professor. My Physics I and II classes were math classes disguised as science. If you didn't know your Trig like the back of your hand, you were bound to struggle.
Calculus is only required for a handful of med schools. Most med schools don't require anything other than six credit hours of math (any math). Trig was a huge part of my Physics class.