> sine is actually how high above the ground you are when traveling around the circle.
That makes total sense, and I wish it would have been explained like that to me, too.
My math teacher in HS spent an hour and a half explaining how derivatives work by just working through stuff on the board after he insisted no one take notes, and it made everything so clear. And reading through the Tau Manifesto finally made me understand what was going on in trig at a basic level.
I totally agree with you about how artificial math education can feel, and I think if larger concepts were introduced more like that many more people would be able to get much better at it.
I read something a couple years ago about how some school was experimenting in a math program starting in 8th grade where they would teach algebra, geometry, and calculus concepts all at the same time. I guess the students were really picking things up fast, and understanding how everything fit together better.
>> sine is actually how high above the ground you are when traveling around the circle.
I learned my trigonometry when trying to figure out how to rotate and move objects around in 2D space for a computer game. I learned then, that sin is responsible for y axis, and cos for x axis.
But I never ever phrased this as "how high above the ground you are when traveling around the circle". I like the elegance of that; things would probably have clicked for me immediately back then, had I heard a sentence like this (and ditto for cosine being "how far to the right are you").
Bottomline, I'm in agreement with both OP and GP here.
That makes total sense, and I wish it would have been explained like that to me, too.
My math teacher in HS spent an hour and a half explaining how derivatives work by just working through stuff on the board after he insisted no one take notes, and it made everything so clear. And reading through the Tau Manifesto finally made me understand what was going on in trig at a basic level.
I totally agree with you about how artificial math education can feel, and I think if larger concepts were introduced more like that many more people would be able to get much better at it.
I read something a couple years ago about how some school was experimenting in a math program starting in 8th grade where they would teach algebra, geometry, and calculus concepts all at the same time. I guess the students were really picking things up fast, and understanding how everything fit together better.