Spaghetti Sine & Cosine Curves
name ______
date ______period ______
Follow the instructions from your teacher and from the back of this sheet
to use your string, spaghetti, and pens to create a sine curve (and then
cosine curve in another color).
Instructions:
1. Carefully wrap the string around the circle bit by bit (starting at 0 radians ending at 2p), marking on the string and on the circle as you go.
· Make sure to mark your starting spot on the string.
· Have at least 4 marks per quadrant (the more marks, the more accurate your graph will be).
· Spacing is not an issue.
· Make sure to also mark at each axis. These are IN ADDITION TO THE 4 per quadrant.
2. For a reference, starting at your 1st mark past 0 radians, number your circle marks #1, #2, #3, …, on the outside of the circle.
3. Lay the string taut (no slack) on the x-axis (below the circle) and transfer the string marks onto the x-axis. Make sure your original starting point is at the origin. Also, transfer the corresponding reference numbers (use the # sign, so as not to confuse with radian measure).
4. Label your x-axis “q in radians”.
5. On the circle, use the spaghetti (ahem, measuring tool) to measure the radius (using an axis is smart), and transfer that length onto the y-axis below (both positive negative). This will be 1 unit (write a “1” or “-1” accordingly on the y-axis). The circle is a “unit circle”, a circle with r = 1.
6. You are now ready to graph y = sin q. Picture in your mind a reference triangle for each of the angles you have marked on your circle.
· sin q = y/r, and since r=1, then with the unit circle, sin q = y.
· Using the spaghetti, measure the length of y for each reference triangle.
· NOTE: if your triangle is in Q3 or Q4, then y is negative.
· Transfer that length to the appropriate height on the xy-plane below.
· Continue in this fashion until you have accounted for every mark.
7. A mean teacher would have had you make infinite marks in each quadrant, so you can picture that if you had infinite marks, all the dots on your graph would be connected. Connect the dots.
8. Voila! You have just graphed y = sin q. Note that you are human, so there is most likely a bit of human error in the graph.
9. Label somewhere near your actual curve a very visible “sin q”. Also, mark 0, p/2, p, 3p/2, and 2p accurately on your x-axis.
10. Major Extra credit: measure your angles on the circle in degrees, and convert each to radians!
Next:
Using the same circle, the same tick marks, the same spaghetti, the same xy-plane on the other side, and the same technique (except now you’re measuring the x length), graph y = cos q USING A NEW COLOR and label it accordingly. Think of a clever way to measure the “x” length without drawing your triangle.
Notes: * when you are in Q2 & Q3, x is negative. ** cos q = x/r, and since r=1, then with the unit circle, cos q = x.