Inverse Trig Graphing

Teaching Inverse Trig Functions, Take 10 (??). Okay, patty paper to the rescue*. I'm hoping THIS year, since we are taking time to construct and ask questions and have a physical thing in our hands that we can flip over and analyze that the students will more readily be able to reconstruct their knowledge of inverse trig graphs.

We started by making an envelope for their notebooks.

 Then we SLOWLY with lots of back and forth questioning created this sheet for sine:

We had to refresh our memory on Inverse Functions in general from previous knowledge. Then we flipped the paper over (after we discussed the "x and y switch roles") by keeping our thumb (positive x) and index finger (positive y) attached to the paper:

And we had a discussion on what part we should restrict the domain of the sine graph to to make this inverse function a function. THEN we shaded the right graph part with a sharpie. 

We did the same with the cosine graph the next day. Then because of a discussion with some students AND the fact that even though we stress that ONLY ONE output is possible, they still are confused with a problem such as:

Without a calculator, find  arccos ( cos ( 200 °) ). 

So after the patty paper, I had them explore with this sheet:

 

 Let's see if THIS is the year the information better sticks to their brain cells.

* Funny note: when we were making the graphs and free-style drawing, a student said, "hey, they should make patty paper lined with a graph/grid". I flipped the patty paper box over and showed her that it really was paper meant to be put between meat patties or some such food.