Timeline for Do I really need to cover solids of revolution in my Calculus I class?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2022 at 1:48 | comment | added | Kevin | @StevenGubkin: Trig functions arguably have more to do with circles and rotating vectors than with triangles. If you stick a unit vector in the plane and rotate it, its x and y components will be modeled by cos and sin respectively (and the path it traces will be a unit circle). So the trig functions act as "translators" between polar and cartesian coordinates, which is handy because it means you can easily switch coordinate systems depending on which is more convenient. But nobody teaches them that way, because it's just too abstract compared to SOH CAH TOA. | |
| Feb 10, 2022 at 17:10 | comment | added | Steven Gubkin | @XanderHenderson The fact that the same functions both give us access to turning angle data into length data for triangles and ALSO model periodic functions is pretty mind blowing. | |
| Feb 10, 2022 at 17:05 | comment | added | Xander Henderson♦ | @SethR I had an interaction with a precalculus student this week very much on that topic. They wanted to know what trigonometric functions (particularly tangents) are good for. I gave a couple of off-the-cuff answers (tangents show up, for example, in aeronautical navigation when computing rate-of-climb, sines and cosines model vibrating strings, etc). I then directed her to a 3blue1brown video on Fourier analysis. The actual topic is likely way over her head, but she seemed excited to know that there were applications. | |
| Feb 9, 2022 at 18:51 | comment | added | Seth R | @ChrisCunningham I struggled with math classes taught that way. Memorizing abstract formulas and techniques is hard and kind of boring. Show me how it's actually used and it is a lot more interesting. Even if it isn't something I would personally ever do, just knowing there is a practical application always got me a lot more engaged. | |
| Feb 9, 2022 at 17:56 | comment | added | Jason DeVito - on hiatus | This. When I read the question, this answer was my immediate reaction. I'm not teaching students how to solve particular problems (whose solutions have been known for centuries, and which have computer implementations which are faster and more accurate than anything a human can do). Rather, I'm teaching them how to think through problems, and giving them useful general tools to help with this process. | |
| Feb 8, 2022 at 22:46 | comment | added | Chris Cunningham | Exactly @AlexanderWoo , and this also explains why it is so bad to teach this topic with "well there are 6 possibilities, so here are the 6 formulas..." which is how many textbooks approach it (and how I was taught). | |
| Feb 8, 2022 at 21:54 | comment | added | Alexander Woo | Let me make explicit something that's implicit in this answer. We teach volumes of solids of revolution for the purpose of helping students learn what integration is about, not for the purpose of students knowing how to calculate volumes of solids of revolution. This should affect how we teach the topic. In particular, a student who has only memorized a formula for doing these problems has missed the point. | |
| Feb 8, 2022 at 19:56 | history | answered | Steven Gubkin | CC BY-SA 4.0 |