The Lessons Of The Unit Circle by Jacquelyn

The Lessons Of The Unit Circle by Jacquelyn - July 2026 Scholarship Essay

“Okay class, today we’re going over, calculating, and memorizing the Unit Circle”. I had always done good in math, so my first instinct was that this would be easy. When my Algebra ll teacher placed the Unit Circle packets on the desks of the others, they whispered “What is this?”, "Absolutely not”, and “How do you expect us to memorize this”. These reactions were normal in my Algebra ll class, but when the packet hit my desk, for the first time, I participated in the expressions. A circle with more than 50 things to memorize in 48 hours; the remaining time before our quiz over it. I had essays to write for English, a statistics test I needed to study for that fell on the same day as the quiz; both of which I procrastinated, and now unexpectedly a Unit Circle to memorize in 48 hours. My mind and heart raced at how I was going to manage to get everything done, and as my teacher began explaining what each value meant and how it was related to a circle I got even more worried. I had no clue what any of it meant.

For the rest of that day I decided to work on statistics as much as possible, I found I learned the material better when I taught it to myself, but this time I had procrastinated so long on teaching it to myself, the test day had slowly emerged. I spent my lunch studying with a friend, and my remaining classes studying as well. I eventually picked up some of the material, so I saved the rest for the next day as I knew if I crammed anymore statistics, I would burn out for the night. To switch the topic and give my brain a break from math, I began writing the rough drafts to my two essays assigned at the same time. I love writing, so the draft was formed in no time, and it was time to begin to study The Unit Circle. As I looked at it, my mind began to race again, and I doubted my ability to get everything done. Instead of questioning myself and why I had procrastinated Statistics and English, I found myself questioning why I needed to learn The Unit Circle. If I wasn’t learning The Unit Circle, I would’ve been able to go back to studying Statistics, or even write my final draft for my essay. After thinking about it further, I realized how silly it sounded that I couldn’t take accountability for my actions, or manage my time better. The circle wasn’t only testing my math skills, but my life and organization skills as well.

As I sat with my sister while she watched tv, she looked at what doing and questioned it. I said I had to learn The Unit Circle, showed her the paper, and explained how I didn’t know where to start. She told me to start with what I know, and dissect it from there so it’s less overwhelming. When I looked at the circle, I recognized the angles and quadrants. The circle was split into 4 quadrants and each one corresponded to a positive or negative x and y value, and the value of the angles increased the whole way around. Knowing this helped me ease my mind as I tackled the material I didn’t know. I started with angle 0, and memorized everything on the line. Then I went to the next and things got trickier. Because to me it didn’t make sense, I couldn’t memorize it. I moved onto the next 3 lines, and after repeating it over again, and recognized a pattern in the values, I moved onto the second quadrant.

The second quadrant scared me. It looked harder than the first, and I felt like none of the material corresponded to the other. Everything seemed to have no correlation, so I didn’t know how to memorize. That was until I looked at the denominators for all of the x and y values. They were the same as the ones in the first quadrant. I skipped to the third and fourth quadrant to see if the pattern remained, and it did. I looked for other other patterns and saw the tangent values outside of the circle were the same for all four quadrants as well. As I spotted more patterns I tried to learn how they repeated and discovered that because a circle as complete symmetry, and geometric triangles that make up the circle are the same in each quadrant, meaning that quadrant has the the same values but increase, and each half of the circle is a mirror of the other. Finding this pattern made it so much easier to memorize the values of The Unit circle. I was able to fill in what I could from memory of the first quadrant, and only had to learn the slight differences that occurred instead of all of the individual values.

Throughout my experience with learning The Unit Circle, I was able to learn to take accountability, manage my time better, take what I know from a situation and apply it, break things down to make it digestible, and even find patterns to learn material. By the end of the week, I did well on my statistics test, finished my essays, and aced my quiz first try.