Students are introduced to the concept of the unit circle. Right triangle relationships are explored to develop an understanding of the patterns involved.
Special right triangles are addressed to help students understand the exact values they will likely be expected to know.
Students often have difficulty with remembering some of these special values. Ask students if they can see a attern that might help them remember that goes with the triangle. Students may point out that there is a pattern of twos—two angles and two sides are the same.
Similarly, ask them how they might remember that goes with the triangle. Students may state that there is a pattern of threes—all angles involved are multiples of 3. Next, once students realize that and go together in an ordered pair, it is easy to point out using a unit circle sketch that a angle involves an value that is and the angle involves a value that is .
Problem 2 – Extending the Pattern
Students use a visual model to extend what they established in Quadrant I to Quadrants II, III, and IV.
It is very helpful for students to think about symmetry as they move on to these other quadrants. Construction of rectangles in the unit circle is helpful for many students to make this extension.