|
(Adapted from a CORD Mathematics
activity.)
|
If you have grid boards such as the
ones shown here, students can easily discover the connections
between the unit circle and the sine and cosine graphs. (If
you do not have grid boards, students can create their own unit
circles by using graph paper, compass and a protractor.)
(This grid board has angles marked every 15º around the circle.
The entire board is approximately 2' by 2' and is made of a heavy
pegboard material.) |
 |
|
 |
Materials: 2 rulers, grid
board, calculator
Data collection: (This activity has students
measuring all of the lengths on the grid boards, instead of
assigning a unit of one to the hypotenuse as in the unit circle.) Using one ruler, join the origin with
the first degree mark on the circle and take the measurement in
centimeters. Since this is the radius of the circle on your
board, you will not need to take this measurement again.
Record this measurement.
Place a ruler in the "y" position and read the "y"
length in centimeters. Leaving the y-ruler in position, use the other ruler to obtain the "x"
measurement in centimeters. The y-ruler will mark the spot to
be measured on the x-axis. Continue finding these
measurements for the entire circle.
|
Discuss with students how to obtain data
at 0º, 90º, 180º, 270º and 360º
Once the data is collected, have students
prepare graphs based upon the columns of data representing y/h and
x/h to
create the graphs for sine and cosine. You can also have students
work with y/x if you wish to investigate tangent as well.
"Using an x-axis scale from 0º to 360º, prepare three separate
graphs using the findings in columns y/h, x/h and y/x."
(For the tangent graph, the y-axis scale will need to be larger.)
Once the graphs are prepared, discuss with students
what is represented by y/h, x/h, and y/x in this activity. If
you prefer, you can have this discussion before the activity begins.
|
