It's funny, this article only serves to remind me how much I've actually forgotten in practice. I don't think I've really done much consideration for trig since my sophomore year of HS. I didn't get into programming via a formal education, and the programming I do doesn't involve heavy graphics or physics so it's just not something I think about. Interesting article, and only serves to inspire me to add re-discovering trig/physics/calc to my todo list on reading.
Obsolete trig functions and why we don't use them anymore (2013)
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Re: Obsolete trig functions and why we don't use them anymore (2013)
#82I'm not that old, but I learned the haversine formula in a marine navigation class I took through (boy) scouts. Our instructor was a retired merchant navy officer who was somewhat upset that the curriculum didn't include it, and deemed that we should know it. My A-level (≈ AP) maths teacher was mildly amused that I knew it and digressed about log tables. We were (I believe) the last cohort to be issued log-tables, bu…
> given the choice in examinations between log-tables, slide-rule, or calculator, we all made the same choice Students would benefit greatly if given a slide rule instead of an electronic calculator for their exams. The former is an effective teacher which viscerally reveals crucial insights, while the latter is pedagogically almost useless; using an electronic calculator to solve problems consists of nothing beyond…
This seems to imagine that the only thing being taught/worth teaching on the mathematics curriculum is number sense.
Firstly, that's not the case. If you want students to answer a problem with any practical application (e.g. money/finance, statistics), or more complex problems where the point is to follow the logic, being able to use the calculator in your pocket is great.
A perfectly reasonable assigned problem might be: add the 7.1% sales tax to this ticket price, do you have enough cash?
And secondly, number sense is easier to teach without depending on particular algorithms.
This is the same complaint as people grumbling about "common core" math, or saying we should go back to the basics of just rote learning times tables and long division.
Students are learning about number sense by different routes now - routes that don't end up with most students blindly trying to follow a particular algorithm with no sense of what is actually happening.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#83These equations are very useful in circular hydraulics. It’s unfortunate I never learned this stuff.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#84Earlier quoted context omitted.
It kind of helps a non Mathie like me doing trig. But I'll ask fof one better: I would love an application that lets me plug in what I have (coords and angles), what I want, and for it to show me how to get it.
Here you go: https://www.geogebra.org/geometry (Press the calculator icon for algebraic view)
Oh this is so neat. Thanks!!
Re: Obsolete trig functions and why we don't use them anymore (2013)
#85I'm not that old, but I learned the haversine formula in a marine navigation class I took through (boy) scouts. Our instructor was a retired merchant navy officer who was somewhat upset that the curriculum didn't include it, and deemed that we should know it. My A-level (≈ AP) maths teacher was mildly amused that I knew it and digressed about log tables. We were (I believe) the last cohort to be issued log-tables, bu…
> log-tables, slide-rule
Is there a difference?
I went to high school well after the rise of calculators. Indeed, only one of my maths teachers had even used a slide rule, so I had to figure the thing out myself. One of the first things was that the multiplication scale on a slide rule is a low precision log-table. The other is why most math and physics problems only asked for solutions to two or three significant figures. (While physics problems do deal with precision, the consistency of the precision is definitely suspect.)
Re: Obsolete trig functions and why we don't use them anymore (2013)
#86Earlier quoted context omitted.
As the math teacher at the first year of university once said: "i know two things: [cos(x)]^2 + [sin(x)]^2 = 1 i*i = -1 but can re-derive all the rest"
From these two facts, you can come to the conclusion that sin(x) == 0 and cos(x) == 1, for any x. I.e., you need to know more.
No, you can't. You can come to the conclusion that if there exits an x with sin(x) = 0, then cos(x) = 1. The expression as it stands is true for every x \in R without any additional assumptions.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#87haversine is incredibly useful when you're doing quick distance calculations between points on the Earth though...
I rely on haversine distance quite a bit and feel sort of disappointed in myself that I never really looked up the background on it before now
Re: Obsolete trig functions and why we don't use them anymore (2013)
#88Earlier quoted context omitted.
I think the point of these was for when they read low-precision values out of a printed table and then multiplied them using slide rules. Even though the article doesn't say it, I can't think of any other practical reason to multiply by adding logarithms.
The log tables let you work without slide rules, which were themselves horribly expensive not too terribly long ago in the grand scheme of things. But yes, this was all about practical calculation , not mathematics for its own sake, that needed to be carried out quickly by people who wouldn't have handy access to machines that keep the dirty arithmetic details (and potential for error) hidden from the operator, wheth…
The converse is true: slide rules let you do calculations quickly and easily (since they hang in the leather holster on your belt) without having to carry an expensive and heavy copy of the rubber bible or similar work and stop and look up numbers then scratch the values down on paper and work the problem.
Re: Obsolete trig functions and why we don't use them anymore (2013)
#89Vers- is just from versus "opposite/against". But versine isn't opposite of sine, if anything it's opposing cosine. I too am curious this how this naming convention arose.
It always bugged me that secant is 1/cosine, cosecant is 1/sine, and cotangent is 1/tangent. Like what does co- mean? Trigonometry never really clicked for me. I can remember the formulas and such, but I never really understood what they meant. It was an exercise in remembering but never knowing.
If you like visual explanations, you might enjoy this from 3blue1brown: https://www.youtube.com/watch?v=yBw67Fb31Cs
Re: Obsolete trig functions and why we don't use them anymore (2013)
#90Earlier quoted context omitted.
From these two facts, you can come to the conclusion that sin(x) == 0 and cos(x) == 1, for any x. I.e., you need to know more.
No, you can't. You can come to the conclusion that if there exits an x with sin(x) = 0, then cos(x) = 1. The expression as it stands is true for every x \in R without any additional assumptions.
Yes, I agree that was badly worded, but in any case you need more than those two equations to do anything meaningful with sin(x) and cos(x).