The relationship, 1 radian is about 57.3 degrees, is developed by utilizing the arcLen( command which measures distance along a curve. Students create a scatterplot of radian measure versus degrees from an interactive real-time, analytic construction, and from real-time measurements, determine the related linear equation using a scatterplot and linear regression. Since the integral which calculates arc length is "hidden" in this activity, it is suitable for students initial encounter with radians.
Before the Activity
Download the attached .pdf or .doc file and read through the activity. The .tns file is self-explanatory and serves as an interactive introduction to the relationship between radian measure and degrees.
During the Activity
It is important to note that tracing the semi-circle definitions can result in undefined values for the arcLen( command if the drag goes too close to the vertical 'gap' near the x-axis. Remind students that data capture is manual and the spreadsheet is set up for only 10 captures. This is due to having to work with a CAS command in a spreadsheet environment.
After the Activity
Ensure students appreciate that radian measure is a ratio of circumference distance to radius and so applies immediately and well to scaling to different radii. Degree measure is not like this and always requires a units conversion before being easily applicable to scaling.