Mastering the Unit Circle

Advanced Geometry students have been establishing a foundational understanding of trigonometry this month with the completion of their Unit Circle projects. The unit circle is the beginning of understanding trigonometry. In the simplest terms, it is a circle on the coordinate plane centered at the origin (0, 0) with a radius of 1 unit. The unit circle is studied through the 30-60-90 and 45-45-90 triangles and all the coordinates and trigonometric ratios that they create within the circle. Advanced Geometry teacher Janet Drake compares knowing and understanding the unit circle to learning the times table for younger mathematicians. “In any future mathematical courses, these students must know these values by heart. So, they have to memorize the circle but also know why those numbers exist.”

To help them learn the unit circle and its values, Janet asks students to create a clever visual representation of the unit circle and its derivations, along with a written mathematical explanation of the derivations. Each poster board must include a central unit circle with angles measured in degrees and radians with coordinates at each point. It must also include five additional circles to show the derivations with each triangle identified. This year’s final projects were colorful and creative as students depicted unit circles as hot air balloons, features on minions’ faces, clock faces of London’s Big Ben, and wacky cartoon characters. While the project helps students commit the unit circle and values to memory, it’s about more than just memorization. Establishing a deep understanding of unit circles is beneficial because when introduced in high school precalculus courses, teachers teach the subject quickly, assume students understand, and move on. The Advanced Geometry students spend at least a week on the unit circle, and then the project helps cement their understanding. Learning the unit circle also equips students with a tool they can use moving forward. “Now students can derive the circle any time they need to,” says Janet. “They can draw the circle, draw the triangles in the first quadrant, and know the coordinates for all the quadrants of the unit circle.”