In my tutoring practice, I've found that the most helpful approach for most students to get through trig in one piece is a "middle way" that combines both memorization and understanding, and I've learned to explain it in a way kids get. A common refrain I often hear from students who are new to Calculus when they seek out a tutor is that they have some homework problems that they do not know how to solve because their teacher/instructor/professor did not show them how to do it. Today, some 800,000 students nationwide take calculus in high school, about 15 percent of all high schoolers, and nearly 150,000 take the course before 11th grade. Also, since memorization doesn't tend to stick, you'll have to keep re-memorizing the unit circle again for every quiz, test and final. Or, a common culture shock suffered by new Calculus students. For one thing, teachers are good at cooking up questions that the unit circle chart won't work on (I work some of those examples in videos below). What’s more important is mastering the prerequisites algebra, geometry, and trigonometry that lead to calculus. However, there are good reasons to take a more understanding-based approach. The fact that it is a straightforward operation to perform means that it can be completed at any time during the process. the "hard way" Many students, frustrated and confused by the unit circle, choose to instead memorize the unit circle chart to get through it, and in the video(s) below (especially the last couple) I give you lots of tips to help do that. Students are not expected to create all of these graphs by hand. ![]() ![]() The "Bowtie Angles"™ (click for FREE printable PDF) Can students explain why there may be differences in the data collected from. The Unit Circle (click for FREE printable PDF)
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