# Activities

• • • ##### Subject Area

• Math: Geometry: Circles

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium

TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 1 from the EXPLORATIONS Book:
Discovering Math on the Voyage 200.

## 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.

• 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