
Touch Mathematics – Trigonometry - kjhughes
http://www.touchmathematics.org/topics/trigonometry
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kalid
Shameless plug, I just wrote about how to learn trig without onerous
memorization ([http://betterexplained.com/articles/intuitive-
trigonometry/](http://betterexplained.com/articles/intuitive-trigonometry/)).

A reader made some simulations based on the dome/wall/ceiling metaphor
([https://www.desmos.com/calculator/az45nwnmis](https://www.desmos.com/calculator/az45nwnmis)).

The right metaphors are essential; I can now visualize the cosecant, where
it'd be useful, and intuit why cot^2 + 1^2 = csc^2. Hope this helps someone.

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saraid216
It's not really clear what "learning trig" actually means.

Trigonometry, as a subject, can be fully understood in a sentence: "Triangles
(especially triangles with a 90-degree angle) have special properties that
make them interesting." This is not useful, of course, and worse, it fails to
justify high schoolers spending most of a year on the subject.

Trig might instead be understood in this way: "Breaking down complex shapes
into triangles makes it possible to find many of the values involved in the
shape, because of the special properties that triangles have."

I _think_ this is a fair summary of the topic. If that's good enough, it might
be worth doing an article based around taking a complex collection of lines
and curves (and draw it out of a photograph for making it feel applicable),
assigning a length here and there, and then spending the entire article
zooming in on specific sections in order to figure out the consequent lengths
of everything else.

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gfodor
I don't think you can get away describing trig in a sentence without using the
word 'circle'. Really I'd argue trig is at its core more about the circle.

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circleguy
What's a circle if not all the right triangles (up to a choice of units)?

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gfodor
Look at the beauty of the sin function and tell me that has more to do with
triangles than the circle. sin and cos are the length of the projected vector
along each axis as a point moves about the circle. connecting those points
forms a triangle, sure, but it seems less fundamental.

~~~
saraid216
I'd absolutely concede that the sine function is more about a circle than it
is about a triangle. If you could really say that the sine function is about a
geometry at all.

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matthewtoast
Author. Looking back at this project now, I think the real takeaway is that
the act of programming can teach. (Even when you program like I do.) I built
this to learn concepts that had always frustrated me in school: fundamental
math that I was fed up, as a 27 year old, never having understood. Building
this really helped me wrap my mind around trigonometry for the first time, and
I still open up this visualization when I need a reminder.

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vlasev
This looks decent but I think it could be made a lot better. Right now it's
kind of messy with all the functions and all the lines and numbers on the
circle there at the same time. It would be better to be able to select those
functions you wish to view.

~~~
vlasev
Reason for disagreement?

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prezjordan
Ha, cool visualization of sec, csc, and cot! Never really knew how they fit in
the unit circle.

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tantalor
Please add support for touch events!

[http://www.html5rocks.com/en/mobile/touch/](http://www.html5rocks.com/en/mobile/touch/)

Because "touch".

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keithpeter
Nice work

As a teacher, what would help make this _really_ useful on (say) an
interactive whiteboard would be

1) On/off by the functions on the bottom left so that I can focus on (say) the
sin function, then switch the cosine function on, then challenge students to
say what happens to sin/cos for various angles then switch on the tan function

2) Line width control or just thicker

3) Switchable angle overlays (degrees for most, radians only for the advanced
ones)

Thanks

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e3pi
A nice simple identity I obtained in high school learning trigonometry:

z^(1/2) = ((z+1)/2)*sin(acos((z-1)/z+1))) for all z

...similar identities may be obtained using atan, etc. This came to me from
the euclidean geometry construction of sqrt(z). I would like to have its
construction image here, but the ascii art is too much. Perhaps Google would
find it. When I messed with it, I noticed for large z, acos()--> 1, it's
argument describes an angle going to zero and `bends' the left edge of the
circle's subtended arc into a vertical line, say, as a zooming magnification.
A dynamic screen as yours would be fun to watch the vertex of enclosed right-
angle(largest) of the sqrt(z) half-chord, as you mouse drag this vertex
around.

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huherto
Pretty cool graphics. But I don't know what to do with or take advantage of
it. How do I validate that I am actually understanding what I am suppose to
understand?

Idea: Can you make a list of questions, exercises, or problems can be answered
by interacting with the model.

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Rzor
>Idea: Can you make a list of questions, exercises, or problems can be
answered by interacting with the model.

This would be great.

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crncosta
This is really a beautiful work, congratulations!

As someone also said here, should have more explanation about the subject
Trigonometry. But I am sure I can show this to a kid and give the explanation
too.

Again, very well done.

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saganus
This is amazing.

I never understood trig to this level. Seeing it geometrically makes it so
much clearer. Very nice.

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Hoozt
This makes me feel like an idiot.

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saraid216
Neat as a reference chart. For amusement, add another dozen trigonometric
functions?

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rupert_murdaaa
/* DON'T EDIT BELOW THIS LINE */

OK

