As a disclosure I haven’t taught trig before. One of my colleagues shared how he introduces it, so I gave it a try and wanted to share out on here also.

Student created a right triangle with a 40º angle.

We talked for a second about how to label each side.

After they found all the different combinations of ratios and then we threw em up on the board to compare.

They were close… but not exactly the same.

Students agreed that all their triangles were similar by AA. And theoretically ratios should all be equal.

I told a great and ancient story of how I once heard that there used to be tables with all these values for each and almost every angle in the back of textbooks. We searched long and hard for said tables but could not find any.

We threw up some general ratios and I told em about how mathematicians named those.

At this point the bell rang… tomorrow we will talk a little more then move onto Soh Cah Toa action.

Let me know what you think/how you introduce trig. This is a year one of teaching geometry sort of intro and I am really interested in how other teachers approach and introduce trig.