Have you ever looked at a word problem and thought "When are we ever going to use this?"? Pre-calculus is the answer! This class is a nightmare for students that hate word problems! Half of this course is solving word problems and the other half is expanding on the small amount of trigonometry covered in Algebra II.
Getting a Grip on Pre-calculus
The first trick is to realize that the 'problem' is like an instruction manual for solving, only it is jumbled up into one paragraph. If you are able to break down each piece of the problem into a short set of instructions, then you can quickly solve almost any pre-calculus problem! Trigonometry problems can be equally reduced by having a very strong grip on the fundamentals. Many teachers provide a sheet with shortcuts and formulas, but with a little extra work you can hopefully reduce this sheet to a status of 'resource' rather than feeling like it is 'essential' for solving every trig problem.
Understanding the Pre-calculus Style
Pre-calculus homework assignments are typically fewer problems than you have experienced before. This is because each one tends to look intimidating. Start with a deep breath and give yourself permission to spend at least 10 minutes on a single problem. Most student will quit without trying and end up not learning anything when the teacher solves the problem on the board the next day. Spend some time on each problem. Write as much as possible. Set a goal of making yourself an 'every' problem solver rather than a 'fast' problem solver and you will immediately see improvement.