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I want to aproach the undertanding of the trigonometric function based on the concept of relacional undertanding, but I have problems to came up with and problemic situation for it. I mean I don´t want the first aproach to the students to be the typical unit circumference thing, I want they to comprenhend the how and why the trigonimetric function pop up the way they do.

For example: I read about some formulas for some geometric objects, there is the formulas and no more; by the other hand, in other place the authors intuitively explaned the notion of area in a rectangle, ans they use it for came up with all the formulas that in the first paper only apear of nowhere (parallelogram, traprice, irregular trapezoid, triangle and even circle).

If someone could recomend me some book to search about this, or give me some orientention. Thank for your time.

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  • $\begingroup$ "by the other hand, in other place the authors intuitively explaned the notion of area in a rectangle" Can you share a link to one of these explanations that you like? $\endgroup$ – Nick C Sep 30 '20 at 2:14
  • $\begingroup$ I don't have the link, i have the archive, and it's written in spanish $\endgroup$ – George Sep 30 '20 at 2:33
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    $\begingroup$ A geometry textbook usually introduces trigonometric functions in the chapter on right triangles, where sin, cos and tan are simply ratios between triangle's sides. Then a first-year physics course reinforces these concepts by solving problems with vectors and their projections. $\endgroup$ – Rusty Core Sep 30 '20 at 3:44
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    $\begingroup$ Why do you want to avoid the unit circle approach? This is a very fundamental means of understanding the trig functions (like why it's even called tangent to start with) and there will be significant resources available about it, depending on where you look. $\endgroup$ – Nij Sep 30 '20 at 3:48
  • $\begingroup$ Because for the student, we have to related with significant context, not in the math it self but with another discipline or the daily life that conects with this and make that significance for the student, but it looks like here there are people that don't apreciatte that way, furthermore i didn't ask for if you belives about good or bad, there are studies that prove if is good or bad and way $\endgroup$ – George Oct 2 '20 at 18:42
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[comment]

Personally, I found the unit circle to be the most intuitive way to think about sin and cosine (and still think of them this way in my head, to this day). Just feels less arbitrary and simpler than SOCATOA. I mean of course, do what you want. But realize, not everyone agrees that you are making things easier for the students. Many would disagree. P.s. see previous questions/answers/discussions on this topic, at this site.

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    $\begingroup$ It is SOHCAHTOA where "H" stands for hypotenuse. When you use unit circle you define them via right triangle with hypotenuse having the length of 1. $\endgroup$ – Rusty Core Sep 30 '20 at 5:17

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