Education Technology

Exploring the Unit Circle

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