Experience First

With this experience, students will extend their knowledge of the coordinates in the first quadrant of the unit circle to the rest of the quadrants.  When thinking of reflecting the special right triangles into other quadrants, students had no trouble identifying when the coordinates would be negative or positive.  Conceptually, they may struggle at first with thinking of the sine as a negative answer since it is a ratio of side lengths, but the diagrams with the reflections should help them make the connections.

​

Formalize Later

When doing the debrief, it’s important to use reference angles to explain why the sine of 30, 150, 210, and 330 are all the same absolute value, since they’re the same vertical distance from the x-axis (30 degrees).  There are many tricks for remembering the coordinates that go with the angles in the unit circle, but it is better for students’ overall understanding of the concepts if they can come up with those connections on their own before teaching them different memorization techniques.