Activity Overview
In this activity, students explore the properties of a unit circle and its mapping functions.
Before the Activity
Select the Cabri Geometry application on the calculator
See the attached PDF file for detailed instructions for this activity
Print pages 1 - 6 from the attached PDF file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity procedures:
Construct a unit circle with origin at (0, 0) and radius of 1 unit
Display the equation of the circle
Mark a point a (x, y) on the circle in the first quadrant and identify its coordinates
Draw a ray from the center of the circle to this point
Measure the central angle (angle formed by the constructed ray and the ray that is the positive x-axis)
Move the point on the circle and measure the new central angle
Repeat for other points on the circle
Record the coordinates of the points and the measure of the central angle
Plot a graph of angle versus x-coordinate and angle versus y-coordinate
Graph the functions sin(x) and cos(x) and compare the graphs
Observe that the amplitude of both graphed functions represents the radius of the circle
After the Activity
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary