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I don't think skipping trig is a good idea. If you want to do engineering, and later take calculus, that trig is really going to help. I didn't have a good trig background going into precalc and it hurt me. Sucks when you are learning new stuff which includes something you never really learned.
It sounds like your CC doesn't offer nearly enough time options for classes. Must be a pretty small school or something. You should see registration at my school. Its ordered based on units completed, and all the good classes are gone by 5:02 am morning of registration (starts at 5am). Its crazy!
Don't skimp on the school. Money is nice, but make school your focus while you can. I am pretty fortunate and don't have to work right now, so all my focus is on school, and it really helps, especially after a few quarters of working + school.
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