In this clip the teacher leads a discussion about why arccos and arcsin gave different results.
Worksheet 6, Clip 1, Discussion of Question 1, 3:20
The teacher leads a discussion about what is given (the output of a trig function) and what is needed (the input of a trig function). As the conversation continues, he also draws the situation on the board. Such a discussion should help the students realize that inverse functions would be useful here.
The teacher sets up equations using sine and cosine and reminds the students of the concept of inverse functions studied earlier in the semester.
The teacher also gives them the notation, which is a convention and reinforces the idea that the inverse trig functions still have an input in radians and an output that are measured in radians.