# 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 Sarah Asmar. 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?

Learning the unit circle can be very challenging for many students. One must know all the elements of the circle and need to know how to apply it. Therefore, I have come up with a few activities to make learning the unit circle more fun and engaging. One activity that would be great when teaching students how to memorize the unit circle and all the elements of it is the game of “I Have Who Has.”  I would create a stack of note cards that would have one element of the unit circle on it. For example, one card will have 90° while another will have π. I will do that for all the elements on the unit circle. Then, I would pass out one note card to each student. One student will begin by saying “I have 2π, who has 0° or 360°?” Then, the student that has the card with those two elements on it will say what they have and ask who has the next element. This will go on until all of the elements have been said and it returns to the student that started the game.  Another activity I found that would help students see the unit circle in a more colorful way is if they created it on a paper plate using colored yarn or colored markers. The x and y axis would be in one color and the rest would be in different colors. They would label each line/angle with the correct degree and radian, and the correct (x, y). Here is the link to a picture of what I would want the students to do: https://s-media-cache-ak0.pinimg.com/736x/74/e9/23/74e9232e7389804ce4df2ea6890e0ff9.jpg How does this topic extend what your students should have learned in previous courses?

Students first see trigonometry in Geometry class as sophomores in high school, but they typically go into more depth during pre-calculus. One way to compute trigonometric functions using the unit circle is by using right triangles. You can find the angle measurement by drawing a right triangle on the unit circle and connect two points. The two special right triangles (30-60-90 and 45-45-90) can be used to form the unit circle. Students would need to recall the rules from geometry to figure out the side lengths of the triangles. With this, students are forced to remember what they were taught in geometry class in order to compute trigonometric functions. If students can see how using the two special triangles creates the unit circle, then it might make more sense to them as where all the measurements/elements came from. How can technology be used to effectively engage students with this topic?

Technology plays a big role in education these days. Students and teachers are encouraged to use technology in the classroom. Khan Academy is one of my favorite websites. He creates very detailed videos about every mathematical topic. I found a few videos on his website to show my students that would help them understand how to use sine, cosine, and tangent with the unit circle. He even has a video that shows a way to remember the unit circle. Another way to implement technology use with tis topic would be with the graphing calculator. Students tend to believe the calculator more than their own teacher. If they saw that the calculator gave them the same exact values as the found using the unit circle, I think they would be amazed and understand how the calculator finds them as well. They might see themselves as smart as the calculator if they can figure out the values by hand and then using the calculator to check their work. I also, might try to find a funny YouTube video that would help the students remember the parts of the unit circle. Once they have the unit circle memorized, it is much easier using it to compute trigonometric functions. Students tend to be more engaged and willing to do something when technology is involved.

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