In this clip the teacher leads a discussion tying the period bar applet to the unit circle.
Sine Period Bar Applet, Clip 1, 1:37
The teacher starts the discussion by having the students recall the meaning of period.
Then, since he has the applet up, he is able to point to a place where the function repeats itself and ask why it is NOT the period. It is important that students be presented with counterexamples to help their understanding.