# Engaging students: Computing trigonometric functions using a unit circle

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Delaina Bazaldua. Her topic, from Precalculus: computing trigonometric functions using a unit circle.

How could you as a teacher create an activity or project that involves your topic?

When I first picked my topic, I was searching through topics that I could choose while playing the game Headbandz with my coworkers. That is when my idea hit me: Trigonometry Headbandz. Instead of asking the traditional questions like: “Am I an animal?” “Do I move?” “Am I famous?” or whatnot, the person guessing would have either a degree value, radian value, or the x-y coordinate on their headband and would ask questions like: “Is my measure in radians?” “Is my measure in quadrant I?” “Does my measure have a radical in it?” For the first few minutes, students would be allowed to use a premade unit circle to help them in guessing. However, after that they would need to guess solely based on memorization of the circle. I think this is a good engage because it is a familiar game that students will enjoy and it’s also educational in that they are subconsciously memorizing the unit circle that will carry them through the remaining months of high school, college, and perhaps, everyday life.

How does this topic extend what your students should have learned in previous courses?

When I was in EDSE 3500 with Dr. Pratt, I truly learned how the unit circle worked for the first time in my life. In high school, it was more taught as: “learn this so you can use it for a really long, hard word that is supposedly math (trigonometry.)” In Dr. Pratt’s class, she gave every student the two special right triangles (30-60-90 and (45-45-90) and an empty circle that had the x-y coordinate plane on it. She asked us to recall what we learned in geometry in high school so that we can figure out the side lengths of the triangle. After that, we formed the unit circle using the two right triangles that she gave us by using the degree measure and the side lengths. It was so neat and so surprising that I have never learned how the unit circle is formed—especially as a math major. I definitely want to implement this in my teaching because it forces students to recall what they used in geometry and it also teaches where the unit circle comes from. In addition, it will also be easier for them to construct it in the future if they were to ever forget it.

How could you as a teacher create an activity or project that involves your topic?

I just love this topic and activities that go hand-in-hand with it, so I decided to do it again. I was in the mood to procrastinate, so naturally I log onto Pinterest. I came across a board game dealing with the unit circle: http://cheesemonkeysf.blogspot.com/2014/07/life-on-unit-circle-board-game-for-trig.html?spref=pi. It is based on the game Life on a Number Line. It caught my attention because it tests the students’ knowledge of the unit circle in a fun way. The game involves game pieces, 3 die (a standard one and two positive-negative dice), a semi-blank unit circle, and flash cards of the trigonometric functions. When a student lands on the radian, they are to name the sine and cosine measurement in order to get credit. This game can also be played on a much larger scale with the entire class competing for extra credit. The whole point of the game is to, as the blog says, “used to living on the unit circle” in a fun and educational way. Like the first activity, Trigonometry Headbandz, it inevitably forces students to learn the unit circle. This way, it’s much more engaging and fun than staring at a piece of paper in hopes of memorizing it.

References:

http://cheesemonkeysf.blogspot.com/2014/07/life-on-unit-circle-board-game-for-trig.html?spref=pi

Dr. Pratt EDSE 3500 class