My Algebra 2 Honors learners were struggling with radians and the unit circle so I broke out the creative guns and went all manipulatives on them. It worked.
The file I used is a PDF I created in Publisher that you can download here from this link.
It is very simple, but very effective. It has a Unit Circle with only the axis marked and 3 triangles with a “finger spot” for holding it in place.
Before I had them cut them out, they wrote the hypotenuse length inside each (which is 1) and the other two side lengths inside as well.
Now the magic occurred. I had them use these triangles with the side lengths written in to tell me the radians and coordinates of the endpoint for each.
All they had to do is move the triangles around, “rotate them” through the angles and use the triangles to document the endpoints.
The connections to “Hey, all we are doing is cutting up a pizza” and “there are clearly 6 pieces of the 30 degree, 4 pieces of the 45 degree and 3 pieces of the 60 degree triangles in the top part of the circle” were immediate.
The harder discussion of the endpoint coordinates were only hampered by the learners that did not follow direction and write the side lengths. Once they had the side lengths in, they saw the connection immediately.
It was nice to be able to have the connections made with the unit circle so easily and now they are all making the unit circle from memory with no problem.