In this clip the class continues the discussion about θ versus the argument of the trig function.
Worksheet 9, Clip 2, Discussion of Question 1, part 2, 4:00
The student asks a question about whether or not it would still vary by 2π even if "it" was 2θ. The teacher does a good job of clarifying her question.
The teacher then puts up sin(θ), sin(2θ) and sin(1/2θ). He then uses these to discuss the difference between argument and input which in this case is represnted by θ.
This can be a difficult distinction for the students and the teacher creates an example to help him explain the difference.
By talking about the argument, it allows the teacher to say the "argument always varies by 2π, then it becomes seeing how θ varies in order to find the period.