[conspire] math {WAS: Re: Password permutations (was: Correction)}
paulz at ieee.org
paulz at ieee.org
Sat Apr 18 10:59:57 PDT 2020
At first, trig would appear to be all about triangles, but wait, there's more. As you have pointed out, trig is also useful with AC electricity. Electricity doesn't have any angles that can be measured with a protractor. However the trig relationships are so useful that we even name some electrical phenomena after them, eg sine waves.
By the time I was in the 2nd semester of trig, the joke with my classmates was that it might take 2 minutes to solve a HW problem, and then another 10 minutes to rearrange the solution to match the one in the back of the book. What the ??? All the practice manipulating symbols and substituting identities is very useful in practical applications to trig, not to mention further math courses. Look up grok.
Here's an interesting trig problem. The roof of a house has a slope A. You want to lean a ladder against the edge of the roof. The ladder has a slope from vertical, let's call it B, so you can safely climb the ladder without falling backwards. As you position the ladder against the edge of the roof, you notice that for both sides of the ladder to touch the edge of the roof, you need to rotate the ladder by angle C with respect to the wall. Make a sketch of the 3D situation where the ladder meets the edge of the roof. For simplicity, make one rung of the ladder meet the edge of the roof. This rung will be parallel to the ground and therefore be rotated by C in the horizontal plane. Making a 3D sketch half of solving the problem. Assume one side is length 1. All of the other lengths will be some multiple or fraction of 1. In the end, you don't need the absolute lengths, just the ratios of the lengths which then define the sin, cos and tan of A, B, and C.
You also mentioned calc. Calculus is about two kinds of problems. Integration is about finding the area under a curve. Differential is about finding the slope of a curve. I say curve, actually it will be some function that is almost never a straight line, but curve is shorter and faster to say. The news latly has had a lot of talk about curves.
<aside>
IMHO, one place math instruction could be improved is this. Calculus class almost always starts off with a long discussion about limits and proving why calc works before actually getting to calculus "problems". This was probably important in past centuries when the calculus was not widely studied and the math department needed to be somewhat pedantic.<end aside>
Integration and differentiation are complementary operations, like division and multiplication or subtraction and addition. Generally division is more difficult than multiplication. After you have worked through a long division, it is comparatively easy to check your work by multiplying. Right?
So, a big clue for the new calculus student. Here is the way that many integration problems are solved. There are actually tables of known integral problems and solutions in "standard" form. You look through the table to find a problem that looks kind of like the one you are trying to solve. Then you try to re-arrange your problem to try to match the standard form. In short, you guess at the answer and then try to prove it is correct! That's were all the apparent busy work in trig class pays off!
On Thursday, April 16, 2020, 10:14:53 PM PDT, Texx <texxgadget at gmail.com> wrote:
How much to pre order one of those shirts? Make mine purple and size Large.
No I only got as far as Algebra-2 in HS and that was undecypherable.
My Trig flunking was in College.
Once you solve the triangle, you can then solve for the arc represented by the angle.Yah theres more than trangles to it, but an awful lot of problems invilve solving in terms of trangles.If you dont get the triangles in trig, you wont get the rest of it either.
I had the understanding that Calculus helps you determint the area under a curve.Someone on here a while back commented that Calculus REALLY helps you determine the area of an irregular surface if you are working in 3 axis.I found that an interesting point. I know better than to ask about using calculus in 4 axis.Ah crap, Calc in 4 dimensions, now Im going to have nightmares.Gee THANKS PAL!
On Thu, Apr 16, 2020 at 9:47 PM paulz at ieee.org <paulz at ieee.org> wrote:
I think we need to order some shirts, "No bad math, just bad math teachers!"
And compounding the situation is that in many schools, it's quite acceptable to say that you are not good at math.
Just to be argumentative, there are a lot of other applications for trig besides calculating triangles.
I am guessing that Texx had trig in high school. There would be no reason for a HS curriculum to assume that students would be using trig primarily for AC circuit theory. Heck, my HS didn't have any classes in electronics.
Anyway, for anyone thinking about learning a math subject, I highly recommend Kahn Acadamy. IMO the presentations are clear and the cost is free!
I'd like to get opinions from anyone else who has tried KA.
On Thursday, April 16, 2020, 2:20:26 PM PDT, Texx <texxgadget at gmail.com> wrote:
Not getting trig can KILL you in AC theory classes.I didnt get trig then, so I was trying to use pythagorean to do polar - rectangular conversion and obviously flunked the test.
The problem was that they started out with all this complicated junk and completely obfuscated the subject.
What they SHOULD have done and DIDNT, was to explain that trig is about arcs & angles.If you have 2 sides and an angle or 2 angles and a side, and you know WHICH sides & angles you have, you can reconstruct the triangle.To me, those 2 lines explain the whole subject most of the way.
I ended up completely learning math up to Calc in 2010 and i now totally get it.I havent taken another crack at Calc yet, though.
On Thu, Apr 16, 2020 at 1:58 AM Nick Moffitt <nick at zork.net> wrote:
On 15Apr2020 06:51pm (-0700), Deirdre Saoirse Moen wrote:
> However, my dad, who could do calc in his sleep (physicist), recommended I skip Trig as it was a waste of time. I believed him. Now, for him that was probably true, but for me, it was not true.
I had a similar problem, where I took calculus twice but *neither* integrated trig properly. I ended up near the end of my second attempt with a burning question in my head, so I finally took it to EFNet #math and asked there.
The first answer came from someone who did not assume any knowledge on my part, and it began: "First, consider the unit circle, and a right triangle with one vertex at the center..."
https://78.media.tumblr.com/tumblr_m93533eyFU1qlfzwoo1_500.gif
I aced the exams after that, because after an evening of flipping through my textbook I found that there WAS a little chapter on the role of trigonometry in calculus. I had taken trig under the name "pre-calculus" but even that class had left the actual POINT behind so early that we just performed recipe application by rote on abstract symbols. I had to re-learn a full year of maths in a single weekend, but it happened at just the right moment to actually stick.
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R "Texx" Woodworth
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R "Texx" Woodworth
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"Face down, 9 edge 1st, roadkill on the information superdata highway..."
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