In this clip the teacher leads a discussion about period while using the applet to rotate two rays around a circle.
Argument Applet, Clip 1, Exploring Period, 2:27
It's important to tell the students which ray reprensents the argument (which the class in this video calls disney). They will then have to identify the other ray as the one corresponding to θ
He gives them an opportunity to identify the other ray and make sense of it. In this case they are dealing with 1/2θ.
Notice how the teacher is attempting to make the period in this case more intuitive for the students by comparing the size of the argument with the size of θ.
He also referes to a comparison between the arclengths, reinforcing this relationship.