Since we only need draw a curve as accurate as our drawing utensils and motor skills allow, all we need is a method to stochastically approximate a sine curve with the box of thumbtacks. Then our method is perfect, it is only the finiteness of the thumbtacks preventing us from achieving a perfect sine wave. Either that, or we must draw one as accurately as any possible combination of these tools allow, and that does not quite seem to be the intent.
Roll the posterboard into a cylinder, use the spoiled milk as a sort of make-shift glue to hold it together.
Dunk the cordless circular saw in the green paint, set it aside. You'll need it later.
Jab a thumbtack into the plywood somewhere at random.
Eat some beef jerky (you'll need the energy for this next bit!)
Take the stainless steel bowl, and dig a notch into the rim with the jack knife.
Woah... that was tough! Also, the jack knife rather looks like it won't be able to do much cutting now. Good thing you already
wizard mathematician, eh?
Using the circle drawing compass and straight edge, draw lines parallel to the edges of the plywood through your thumbtack.
Starting with the notch in the bowl at the edge of one of the lines you drew, roll the bowl to the thumbtack, turn it 90 degrees, and then roll it to the edge. Take note of where on the bowl the edge of the plywood is touching.
Eat one of the apples, because, really, what else are they good for?
On the floor, using your circle drawing compass and straightedge, draw a graph to the best of your abilities.
Use the magnetic compass to figure out where north is, in case you get lost.
Stop and think for a moment.
Have a drink from the bucket of water, since you've been doing so much work and you're thirsty.
Now you silly, all that puttering around you did and you've knocked over the bowl, and you lost your measurement, you'll have to start again.
Duplicate your graph using your circle drawing compass and straightedge. (Yes, on the floor again.)
Drop a thumb-tack on the duplicate graph.
Draw horizontal and vertical lines through the thumbtack with your circle drawing compass.
Roll the bowl along the line as if it were a wheel, starting with the notch at the edge of your graph and stopping when it's on the thumbtack. Lie it down when you get there so that it's touching but not crossing the line. (You don't want crossed lines, they hold grudges for a very long time)
Make a mark at the notch.
Using your circle drawing compass and straightedge, copy the horizontal line form the edge of your duplicate graph that you started rolling from to the thumbtack, to the bottom of your original graph.
Copy a vertical line from your duplicate graph (again, using your circle drawing compass and straightedge) from the bottom of your duplicate graph to the edge of the line you just drew. Make sure it is again vertical.
Have another apple, because really, why else would you have been given a freaking apple? Does it have a PhD in math? I DOUBT IT! Eat the blasted thing.
Put a thumbtack on the top end point of the line you drew. You have completed the first point on your curve!
Pat yourself on the back for successfully demonstrating that your method will eventually approximate a sine curve to precision limited only by your tools and skills. (Specifically, how good your eyesight is to see that the bowl is indeed on top of the thumb tack, how round the bowl really is, how large the radius of the thumbtacks are, how carefully you can roll the bowl and lie it down, and some other totally unimportant factors considering the potential for measurement errors already... but these are all merely physical limitations! Your method itself was superb!)
Now, take your freshly painted circular saw, and deal with the evil
wizard mathematician once and for all!
Oh, and have some more beef jerkey, mmm, tasty!