I haven't had to do a single free body diagram since Physics I freshmen year of college. Holy crap that class was awful. My first physics class, I didn't know how to do anything....half way through the semester.
The classes are standardized so that all the physics I professors would assign the same syllabus, same homework (Mastering Physics anyone?), same awful awful textbook and same tests. I'm convinced the physics department at my school had some sort of endorsement from that textbook company if they required those textbook/software package for classes.
So today I stumbled onto some problems that required me to use free body diagrams (had to google 'free diagram physics' to figure out what the real word was because I forgot there was a 'body' in there). I found a rather intuitive answer to my questions about when to use sine and cosine in free body diagrams. Believe it or not, four years later I still didn't have a clue until today. Thanks kirchwey of Yahoo Answers!
Quoted from Yahoo Answers:
To a large extent, common sense can help. Think of the force applied by gravitational force to a ramp, mg, always straight downward. If the ramp is horizontal (θ = 0), all the force (1 * the force) is normal to the ramp. If the ramp is vertical (θ = 90 deg) none of the force (0 * the force) is normal to the ramp. What function = 1 at 0 deg and 0 at 90 deg? The cosine! So we can say Fn = mgcosθ. Similarly we can go through the same mental exercise to determine that Ft (tangential or along-the-ramp force) = mgsinθ.
Just a couple of examples, but you can apply the same thinking to many other problems. Sometimes you'll find a function going to infinity, like the horizontal force needed to push a weight up a ramp tilted to angle θ. At 90 deg you just can't push uphill by pushing horizontally. That's a tangent function. F(hor) = mgtanθ. No force (assuming no friction) at 0 deg, infinite at 90 deg.
Source Link: http://answers.yahoo.com/question/index?qid=20081221044552AAsmlSv
