Precalculus Project decision OK so I have to do a research paper/presentation on an experiment/project that relates to my precalculus class.  Only problem is that I was given no topics to choose from and I couldn't find any real good ones online.  Can anybody give me some good ideas/topics that I can do? (P.S. if its fun then that's a plus :D)
 A: I have no idea what does or does not relate to your precalc class. But I hope that the construction of 3d figures as stacked 2d images fits, because I think it's very beautiful.
For instance, .
Depending on the things that you do in your class, these shapes might be different. But I think they're beautiful and fun. If you're very careful, you can even approximate certain volumes by adding up the weights of the pieces of paper (or whatever material), which suggests some deep things in math. Like calculus, in a way.
Or perhaps I'm completely off mark - just an idea.
A: When i was given a similar choice, i chose this, seemed fun and also pretty useful
http://en.wikipedia.org/wiki/Inclinometer
will take some effort into building it, but is a good idea nevertheless
A: For some fun, how about jump rope, or if you can recruit a couple more partners, Double Dutch?
Use a camera to take some pictures of the activity, and print them out to analyze and include in your report.  What is the shape of the image of the rope?  Perhaps it resembles part of a sine wave, or a parabola.  Try it with the rope in motion, and also just dangling from two hands.  Does it matter what angle the photograph is taken from?  Does the distance of the camera from the rope change anything?  What functions you have learned about fit the image of the rope most accurately?  Do certain functions fit better than others under different circumstances?  Can your formulate a hypothesis explaining the results?
If you have a digital camera to bring to class, you can repeat the experiment while giving your report, and I imagine this would make for a lively demonstration.
A: You could do something with trigonometry. I remember playing the “hand rule game”. This is a game that helps you remember the sine and cosine of $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$.
The game consists of the following:
Starting from little finger to thumb fingers, assign the five angles commonly encountered in early trigonometry.
Little finger – 0, ring finger – 30, middle finger – 45, index finger – 60, and thumb – 90 degrees.
Ensure that the palm side is up while assigning.
Now, the trick is the (square root of the number of fingers below the angle finger) / 2 is the value of sine of that angle. Thus, the sine of 30 degrees is the square root of 1 divided by 2 = 1/2.
Demonstrate this trick first and then design a quiz based on it. You can play a rapid quiz with friends in a group. A volunteer displays the cue angle by marking it on the finger and the others tell the answer. It can help create a shortcut to calculations and save you a lot of time in exams.
