Trigonometry For Beginners!

[shopandmath]

Trigonometry For Beginners!
Video link

[mklotz]

"Exaples" ? Will the sequel include a discussion of proofreading ?

In any discussion of trig, it's worth first discussing if a triangle (and they aren't all right triangles) can be solved. Any triangle contains six items of information - three sides and three angles. If any combination of three of those, of which at least one is a side, is known, all the others can be found.

It's important to not leave the student with the impression that, if he learns to solve right triangles, he understands trigonometry. He'll be lost the first time he encounters a triangle without a right angle unless he's been introduced to...

sum of the angles = 180 degrees
law of sines
law of cosines

[DIYSwede]

Nearly 50 years ago, in math class our teacher claimed that "EACH triangle has 180 degrees as sum of its angles".
Being a smart-ass kid (as I was, even back then) I thought about that and returned a few days later, smugly stating:
"Assume a triangle with one point at the North Pole, and its other points on the Equator at 0 deg meridian and at 90 deg E (or W).
Now this would be a triangle with an angular sum of 270. -Right?"

My teacher dryly remarked that his 180 deg sum was for PLANAR geometry, and that we should stick to this for another 5 years...

A few years ago, my then 12 year old daughter commented on my swearing as I burned my hand at 65 deg C in the dishwasher:
-"Good thing you didn't put the hand in the corner then, Daddy - as it's ninety in there!"

-What goes around, comes around...

[mklotz]

Nearly 50 years ago, in math class our teacher claimed that "EACH triangle has 180 degrees as sum of its angles".
Being a smart-ass kid (as I was, even back then) I thought about that and returned a few days later, smugly stating:
"Assume a triangle with one point at the North Pole, and its other points on the Equator at 0 deg meridian and at 90 deg E (or W).
Now this would be a triangle with an angular sum of 270. -Right?

Reminds me of a problem I constructed for some math students I was attempting to help.

I walk a mile south, then a mile east and then a mile north and I'm back where I started. How many points on earth exist where that is possible ?

[shopandmath]

Hi Marv
is there a typo of a mistake that i missed?
you are right its not all of trig just the beginning
there was a large amount left on the editing floor (maybe to much)
this is for Y2 GM class some of the students have been out of school for some time
I tried to do a "its ok - feel good" intro before we start the complex problems
thank you for you comments
Ray

[DIYSwede]

Reminds me of a problem I constructed for some math students I was attempting to help.

I walk a mile south, then a mile east and then a mile north and I'm back where I started. How many points on earth exist where that is possible ?

At one and only one point, Marv - coincidentally at the very same place where an imaginary cabin would have all its four walls facing south.
Re:My bold italics in your quote: -Would you say that the students of yesteryear were less "resistant to counseling" than today's?

Cheers
Johan

[mklotz]

At one and only one point, Marv - coincidentally at the very same place where an imaginary cabin would have all its four walls facing south.
Re:My bold italics in your quote: -Would you say that the students of yesteryear were less "resistant to counseling" than today's?
Johan

There are an infinite number of points where such a walk is possible.

The North pole is obviously one of them, but consider the following...

Draw a small circle around the South pole such that it has a CIRCUMFERENCE of one mile.
One mile north of this circle draw another, larger circle around the pole.

Start at any point on the larger circle. Walk a mile south and you're on the smaller circle. Walk a mile east (or west) and you'll return to the point from which you entered the small circle. Walk a mile north (thus retracing your walk south) and you're back where you began on the larger circle.

Since the larger circle has a mathematically infinite number of points from which to start, the answer to the original question is an infinite number of points.

The "students of yesteryear" have become the adults of today. Most of them will go to insane lengths to avoid anything remotely mathematical, often trumpeting their ignorance, presumably to demonstrate how like their fellows they are. Based on that, I leave it to you to imagine how they were yesteryear.

[shopandmath]

I could be visualizing this wrong
If I went one mile north then one mile east wouldn't i have to go 1.4 miles south - west at some point to get back to where I started ?