Examples of concepts and how to work on improving understanding. Sin. What is sin? How does one explain it to someone who never heard about it before? Is it just a ratio (opp/hyp)? If so, why is this ratio so important?

 

Well, when we write it, how do we write it? Say we have an angle A°. We write it as sin(A°). This does not look like a ratio! It looks like a function! They learned functions: f(x). The sin is a function! Let them take out their calculators and look at various values. Then draw the triangles and ask them if the results from the calculator make sense. Ask them to find sin(0). The calculator will say 0. Ask them to explain it.

 

A Google search on sine, gives this site: http://mathworld.wolfram.com/Sine.html. It states: “The sine function is one of the basic functions encountered in trigonometry.” Note that sin is a function, not a ratio.

 

This particular article then goes on with very complicated stuff. The point is for one to read the article, and to focus on the beginning of the article, before it gets complicated. Here we will see the stress on sin being a function. This is then how we teach it. We say it is a function, as every angle has one value of the sin. We show this by drawing the triangles.