# How to introduce trigonometric ratios (HS) through a cognitive model?

I'm teaching a precalculus course and also taking a class on how to teach mathematics constructing a specific cognitive model for different topics. So, I have this assignment to build a cognitive model where I have to introduce my students to Trigonometric Ratios but in a constructive approach. One of the condition is create different kind of exploration activities where the student should be able to conclude properties and ratios till the only thing that’s missing are the names of the relations (sine, cosine, etc.), now I’m kinda lost here because I always being teaching this in the traditional way, Pythagorean theorem, special triangles, sohcahtoa, and so on.

What I have now is the idea to make them build several equilateral triangles. First make them realize the relation between the measures on the sides when we cut in half, then using triangle similarities try to make them realize on how they always get the same proportion.

Anyone has implemented something like this in your classroom? Where I can find information on the matter? No luck so far and any help is very much appreciated.

• (1) I'm not sure that "a constructive model" is the best way to approach what is a rather tricky and new topic for most kids. Not sure that it serves the need best. (2) I actually prefer using the unit circle to start with, more so than ratios, since the algebraic complexity is less to start with. – guest May 24 '18 at 20:29
• It is true, but the idea is to explore (and create) activities that may serve to that purpose. – Grouper May 25 '18 at 2:40
• Not sure if constructive enough, but I tried the following with one class after covering similarity: Have all students draw a triangle with a given angle but arbitrary size. Have them exchange only the length of the longer leg with their neighbor who has to calculate the other sides using only his drawing. – Jasper May 25 '18 at 16:30
• Grouper: Fair enough--have to explore ideas. Not fully formed concept, but probably trig evolved from practical problems of mensuration so perhaps an application would be a helpful framework. – guest May 26 '18 at 19:33