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.