Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Trigonometric Functions

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™ CAS

2.1

## Radian Measure - An Analytic Approach

#### Activity Overview

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.