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I always yearned to understand a practical reason to learn calculus. My teacher at college was a German woman that spoke English with a thick accent. Her joy for the course seemed self-evident, but she failed to ever share a real-world reason or application for what we were trying to learn. 45 years later,I still haven’t used what I “learned”, or ever came to understand why we did.
This has always been my biggest gripe. I took linear algebra for 1 semester and while I passed, I never understood the point. Next semester I took computer graphics and everything clicked. I had a simial experience with taking Calculus and Physics. It only made sense once I understood the application.
No one knows what a 12 year old is gonna end up doing with their life. It's better to give them as many tools so they have the opportunity to follow through with something. A kid wont grow up to be an engineer if they didn't learn geometry fundamentals in middle school, or a nurse if they didn't learn basic anatomy, or a chemical engineer if they didn't learn how chemical reactions occur.
Calculus is how I think about physics, and specifically used in almost every way I physically interact with the world. When thinking about whether to accelerate to pass someone, be it walking or driving, that's calculus.
It's the highest level of that math that comes intuitively to me, and I suspect that's why I think in it. I suspect smarter people than me go through life intuitively thinking of everything in higher forms of math.
I use sin all the time.
If you listened to music, your phone used them about a billion times. ... well, not exactly since more efficient algorithms than full perfect computation exist, but...
Same for GPS, cell signal processing, camera functions... They're all over the place. Taking that picture required it.
While it is necessary to understand the background, digitized sampling and Fourier transforms of the data don't calculate sin/cos/tan.
Like I said: more efficient algorithms have been figured out. That doesn't mean those equations are magically meaningless or not involved conceptually. Trigonometry is everywhere, doing important things.
:cries in arctan2:
Im basically a mathematician and never use trigonometry, but I use a lot of probability and statistics every day at work.