Not me. I went years without until last week I realised I needed them for a script that points an object at a target in Maya. Turns out trig is really fucking universal.
A^2 + B^2 = C^2 is known as the Pythagorean theorem. This theorem explains the proportionality of the 3 sides of a right triangle (a triangle with 1 corner angle = 90 degrees). If you know the length of 2 sides (in his example, the wall beams) you can find out the length of the third (in his example, this would be the supporting strut spanning the beams that meet at a 90 degree angle). If their example is explaining a beam that spans the room from 1 corner to the other, you still use this formula as a rectangle is 2 right triangles that meet along their hypotenuse (the longest leg of a right triangle, or the length you are solving for in this problem). The 2 known sides are the length/width of the room, and you solve for the 3rd side, your diagonal beam
Completely fair point, that I do not think I have the knowledge to speak on. On the Trigonometry Wikipedia page, he pops up a few times, and many trig identities are known as pythagorean identities. Perhaps its not fully trig, but was used as a basis to help discover trig? Without having the understanding pythagorus gave mathematicians regarding triangles, I would think it would be pretty hard to begin developing deeper math regarding said triangles
Squaring using 3+4=5 is one of the oldest relationships used by masons. don’t need a ruler, just a piece of string or straight edge. Pythagoras described the relationship on paper
One day, while working on a website, I was wondering how to calculate a specific point in a graph. After googling, the answer was by using sine and cosine. Mind blew away, I had always thought I’d never use them.
Since becoming an adult it has become increasingly obvious to me that early high-school level stuff is impossibly complex for a significant chunk of the population.
It’s unfortunate that you are correct. However, when it comes to memorization, trig seems pretty tame. That one mnemonic just about covers it all. Even multiplication tables seem like a larger memorization effort to me.
Not really. The point of getting really good at it in your teenage years is so that when it shows up 30 years later you have a vauge idea of what you’re looking at and can figure it out again. If you had only a surface level understanding to begin with, it’ll all be totally gone by the time you need it again, and very few people have the gumption to teach themselves a subject from scratch.
The reason they drill it in to the extent that they do is so that you have a foundational understanding of the underlying math on which to build new knowledge. If you show up in calc 1 in college without remembering even the basic concepts you were previously taught in things like trig…that can really bite you in the ass. My teacher LOVED pulling out classic substitutions for Secant, Cosecant, and cotangent (No, i didnt outright remember them from Trig, but I had seen them, and that made refreshing much easier). Also these concepts then form the basis of many other fields such as physics (electricity/magnetism, kinetic motion, optics, etc.), chemistry (quantum, MO theory, and things relating to the physics side of why chemistry occurs), and many of the graphing concepts used in engineering/stem only make sense if you have the foundational understanding of what integration/derivation are. Those stem from understanding how to graph complex functions by hand (like we did in trig) so that when you are doing it later with assistance, you still GRASP what is going on.
Yes its not perfect, and yes for people who never need that later in life it can suck. However, I would make the argument it is better to have more of your population educated to a higher standard than what is needed in daily life, than to only give that to those who are aware enough at a young age to actively seek said education
Personally once you got to the Cos Sin Tan and Log part of math in grade 11 and 12 no amount of practice ever improved my understanding of the underlying principles. Once most of the work gets done in the calculator or computer I just lost sense of what was happening in the background. It’s just turned into put number in calculator and get answer. But that’s probably just a failing of the local school systems methods or the individual teachers maybe.
There will be those that do and dont get the “nitty gritty” of the theory side of the math. Those people sometimes become math majors. Normal people (joking, dont be mad math majors), need more than simply the theory side of the math and actually need to see/perform the application side of things. I never once “understood” the lesson in math class when we go over the equations with variables only. I only truly began to learn the material and be able to use it once we got to the example problems. We would do multiple in class and then I would understand how to literally go through the problem and perform the math that was expected of me on the homework, and subsequently the test. There is tons of stuff i know how to use in math, but by no means understand WHY it came to be, or HOW its works for the realm of mathematics. I wanna know how this math can help me solve real life problems, problems I will face in industry, or even just a cool way to apply math in the real world. Not how it will be used in research to find new types of math we wont be able to apply for 70 years.
It was pretty funny being in calculus in college. I was in a class with mostly engineers who were also taking the exact same weed out courses, and nearly every day after the professor would finish showing us the theory side of the lesson, hands would shoot up and the question of, “What application does this have in real life or engineering? Like, how will I actually use this?” always got asked. So not “loving” the theory is by no means uncommon (we all wished for an application focused version of the class to exist, for people like stem students who are not into the math theory lol), but I still see the value in having it presented so that you can have a more foundational understanding instead simply going through the motions
1209 is 3 times 13 times 31, and cats are better at typing than they are at math.
In base 10, the sum of the digits of any number that is divisible by 3 is also divisible by 3, so 1+2+0+9=12, implies 1209 is divisible by 3.
Likewise, 1001 is divisible by 13, so if you split a number in base 10 every 3 digits, and subtract/add alternating sets of numbers, if the result is divisible by 13, the original number is, too. 209-1 is 208, which is obviously divisible by 13, so 1209 is, too.
Divisibility by 31 in base 10 is harder to check, but 999998 is divisible by 31, as is 999999999999999, so you can just split the number every 15 digits, and add those together, and if the sum is divisible by 31… I’m talking about math to a cat.
did you know that adding up all the divisors of 1209 and swapping the last two digits gives you a number that can be represented as the sum of two cubes in two different ways? or maybe not, I’m just a cat :3
I’m might be splitting hairs, but I would argue by virtue of using a machine that uses trig, an individual is using trig, though abstractly. I’m sure you’re brother is dumb, yes.
Best take right here. Trig shows up a lot when you actually do stuff. Woodworking, programming, physics, art, music, philosophy. Math shit is universal human language.
The other fields I get (trig is insanely useful), but how the bloody hell does one use trig functions in philosophy? Are we gonna be triangulating the border of science to solve the demarcation problem?
Math is philosophy, and trig does a very good job of describing the world we experience. The unit circle, right angles, pythagorean theorem, sinusoidal damping, etc, are all pretty philosophical concepts. What else could the be.
Don’t tell yourself that, unless you’re just not that interested. It takes more work and catering some creative solutions, but it is worth it. I got an engineering degree before I was ever even diagnosed or medicated.
I’m totally not interested in math stuff, like at all. If I need it for what I’m trying to do, or if it greatly helps me with it, I still end up learning it anyways though :) People often say that learning in practice is the best way and I feel like that is even much more true for me personally. I’m goal oriented af, and I make all those goals myself based on what I want to do. If I really really really want to do something, there’s nothing that will stand in my way, I’ll find a way. I’m the type of person to get frustrated and say “fuck this I give up”, only to be back at it after 30 mins because giving up isn’t actually something that exists in my head haha.
So no need to worry about me telling myself that. I guess I was thinking from the perspective of just studying it because of studying it, which yeah is basically impossible for me unless it’s just something I’m really interested in and I’m stuck browsing Wikipedia at 3AM. Thanks for the encouragement though, nice stranger! I really do appreciate it.
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