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.
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.
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.
And guess what? You found it out without having to memorize the process until you knew it by heart.
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.