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Turns are better than radians

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491–494 of 494 posts

Re: Turns are better than radians

#491
post #202
post #183

Earlier quoted context omitted.

I'm a 50 yo programmer. I have a CS degree. I don't even remember my college calculus much less my high school trig. I just haven't had cause to use it in my career, not as a sysadmin, not as a programmer. My son is taking calc 3 and I knew I happened to have my calc 3 notes from the mid-90s, so I pulled them out of the filing cabinet and my very carefully taken notes, my proofs, my hand drawn graphs, it was all gibb…

By far the most annoying myth I face when trying to discuss the pros and cons of various education techniques is the pervasive idea that everybody is a magical knowledge sponge and will go to their grave still remembering how to integrate by parts and every detail about some particular battle they covered in seventh grade, and therefore, if we slightly tweak a curriculum plan to drop something that was included on th…

>>> simply isn't anything to be done about that if you're talking about humans and not some homo educationous who mythically retain all knowledge they were exposed to even for 30 seconds just as the mythical as homo economicus perfectly rationally conducts all their economic business at all times. Perhaps they're actually the same species.

Yeah they belong to the genus homo mythicus

Re: Turns are better than radians

#493
post #112

Indeed, maths never "decreed that sine and cosine have to take radian arguments". But thinking that makes any sort of point is a fundamental misunderstanding of maths. There are infinitely many sinusoidal functions out there. You can just adjust amplitude, frequency and phase to your heart's content. Trigonometry basically requires that sine and cosine have specific amplitudes and phases, but gives not one shit about…

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Re: Turns are better than radians

#494

Earlier quoted context omitted.

This is a very good point, but it took me a minute to get what you were saying beneath the snark. Translating without the snark: There's a famous equation relating sin and cos to complex exponentiation. It also helps explain the Taylor expansions of sin and cos, which is one way to compute them and to find properties about them. It's a very important equation. It is: ix e = cos x + i sin x kazinator's point was that…

Perhaps an even nicer equation: 1^x = ncos(x) + i nsin(x) using a multi-valued definition of the exponentiation on the left hand side.

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