This activity introduces Radians as the arc length around a circle of radius one unit and the equivalent angle measurement. Students are then provided with a unit circle on the Cartesian plane to see how the arc length relates to the distance to the x axis (sine). Students are provided with interactive content to help explore this relationship.
The aim of this activity is to provide students with a better and more intuitive understanding of radians as distinct from necessary conversion from degrees to radians without any reasoning.
- Arc Length
About the Lesson
What is a radian? In this activity students explore radians as the length of an arc on a circle of one unit. Students drag a point (P) around the unit circle and see the radian and degree measures accordingly. In the second stage of the activity students also study the distance of point P from the x axis (sine) and align this to the arc length (radian) measure. Conceptually this is a different approach but helps students move away from the typical approach of converting an angle in degrees into radians, instead they are able to see both the direct relationship (arc length and sine) or indirect (angle, arc length and sine).