Teaching the unit circle to Algebra 2 students involves a LOT of information! This survival guide walks students through the special right triangles, drawing angles on the plane, defining radians, and finding the sine and cosine of angles on the plane.
Students then create a table of values to use for their unit circle, and we construct a unit circle from scratch using a protractor and a compass and all of our information the last day. This is a 3 or 4 day lesson depending on how much extra help students need on specific skills.
I have found that trying to place meaning behind the unit circle can be difficult, but having the prerequisite knowledge is a must.