The class in which I envision using this sketch is high school trigonometry/precalculus.
Topic being studied: graphic representations of sine cosine and tangent (elements of trigonometry).
Mathematics behind this sketch: see text in each worksheet.
The usual way it is taught is one section at a time rather than combining all three sections into one lesson (algebraically, geometrically, and transformationally).
Enhance the way of learning by: giving a better visual of what all these terms (transformations, arc length, etc) actually mean and represent in relation to the unit circle.
I would imagine using the sketch by: through independent study at home online or in the classroom as part of a lecture. I wouldn't have the students construct it necessarily, but I would have them observe the sketch, and maybe it would include a demonstration of the radians.
Act out how you would introduce the lesson and what you would expect would happen: I would discuss the trigonometry of a unit circle and relate it to how that would appear on axes. I imagine the students would be much more engaged and visually aware of the concept.
Common Core Standards: standards 5 and 7
New functions of Geogebra: transformations using vectors and creating check boxes to better organize what we want the audience to understand.
I learned this about math: what radians actually are and represent and how to construct a sine graph based on the unit circle.
I learned this about pedagogy: There are so many ways to use technology in the classroom, as well as many ways to teach a specific topic. For example, I've always memorized the properties of trig graphs, but this worksheet demonstrates the foundation of trig graphs based on the unit circle.