Large Scale LAB for Creating Sine Curves Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

Here is an idea to consider if you want to produce a large demonstration of the creation of the sine curve, or if you want students to develop large display size murals of the sine curve.

Materials:  butcher-block paper (or large pieces of construction paper
                               - the kind that comes on the rolls)
                        a blackboard compass (or a round bowl for tracing)
                        a protractor
                        string
                        narrow strips of colored paper cut on a paper cutter
                           (or pipe cleaners, dried spaghetti, string licorice, straws)
                        markers (might as well make it colorful!)
                        glue sticks (or scotch tape)
                        scissors (if using paper strips or straws)

Directions:
1.  Lay the butcher-block paper on a flat surface or attach it to a bulletin board or wall.  If you are using this activity as a demo at the front board, you can work right on the board without using the paper.  (If you are doing the demo, have the students come up to do the measuring.)

2.  At one end of the paper, draw a large circle with a blackboard compass.   Draw a set of axes on top of the circle. 

3.  Using the protractor, mark the circle every 10º (or 15º) starting at 0º.

4.  Adjacent to the circle, draw another set of axes with an x-axis that is the length of the circumference of the circle.  Use the string to determine the circumference of the circle.
                          

5.  Place the string around the circumference of the circle with one end at 0º and transfer the 10º (or 15º) marks onto the string using the marker.

6.  Stretch the string along the x-axis on the axes to the right and mark off the 10º increments.  You may wish to also have the students label the axes in radians.

7.  Using one strip of paper, determine the radius of the circle (cut the paper to match the needed length).

8.  Using two additional strips of paper, cut the strips to form a right triangle on the circle where the radius becomes the hypotenuse.  One side is vertical and the other is horizontal as seen below.

9.  Transfer the vertical paper strip to the axes on the right and glue it in its proper degree location.  Magnetic strips of paper can be made ahead of time for use on a magnetic blackboard if you are doing a demo (buy magnetic tack-on tape in any craft department). 
 
     Be careful to position the strip above or below the x-axis depending upon the
     quadrant you are in (if the strip is above the x-axis in the circle, it will be above
     the x-axis on the graph and vice versa.)  You may need to help students figure
     out what is happening at 0º, 90º, 180º, 270º, and 360º.

10.  Repeat this process for all of the degree marks around the circle.

11.  When you are finished, you will have a pictorial representation of the sine curve (by using the vertical strips), or the cosine curve (by using the horizontal strips).