Precalculus: Radian Measure

Objectives

• Students will describe the relationship between a central angle, the radius, and the arc length of a circle.
• Students will recognize that changing the radius of a circle does not affect the proportions in the circle.
• Students will convert an angle measure from radians to degrees and vice versa.

Vocabulary

• central angle
• exact value
• radian
• right angle

About the Lesson

This lesson involves exploring the relationship between the central angle, the arc, and the radius of a circle.
As a result, students will:

• Use a slider to change the radius, and conclude that the relationships are preserved.
• Form a definition of a radian.
• Drag a point to change the measure of the central angle to discover the relationship between radian and degree measure.
• Create a proportion that can be used to convert the measure of an angle from degrees to radians and vice versa.