## Thursday, November 17, 2011

### Precalculus Trig Function Transformations

We've just finished a unit on transforming trig function graphs:
y = a sin b(x + c) + d.
We did various things and practice, but I think I found my new BFF towards the end of the unit once we were reviewing for the test.

A student was having a hard time looking at a graph of a transformed function and getting the equation. I had some old transparencies that had the coordinate plane on it with radians on the x axis. I also had half sheets of cut up transparencies and a ton of markers. I laid the 1/2 sheet over the graph and had the student draw the parent function of the sine graph (for example). Then she was able to slide the 1/2 transparency any place she wanted to see what the transformed graph would look like (barring amplitude and period changes ...... though I guess we could have used another 1/2 transparency overlayed on that one).

This seemed to help gel in her mind the steps she had to take. I think next year I may give all students such transparencies just to keep and play with for the duration of the unit. .... My 2nd thought was to have pipe cleaners they could manipulate into the shapes and then move those around on a graph.

Also, I loved this particular review question I gave. There was a picture of a (say a potential sine graph) that has been transformed in all sorts of ways. The question was: find 2 possible equations for this graph. I guess a variation question could be: find a sine and a cosine equation for this graph ... or find 2 sine equations and 2 cosine equations for this graph.

1. Patty paper might work as well

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3. The Sine and Cosine curves are actually each other exactly but out of phase by 90 degrees. If you were to displace the sine graph to the left by 90 degrees, you get the cosine graph; if you push the cosine graph 90 degrees to the right you get the sine one. Hence the identity sin (90-x)=cosx and cos(90-x)=sinx .

Thats a really lovely teaching method about transformations you got there in your post; I always check in here to learn more about innovative teaching strategies as well as experiences. Thanks for this blog. Peace.

4. Richochet ... that's an intriguing idea, and I have tons of patty paper because of geometry.

Whitecorp ... thanks :)

5. No problem Ms Cookie. Btw I don't know if you do guest posts? I would be extremely delighted if you are willing to write something for my site.

6. Hi Whitecorp,

Eeeee, "guest post"? Never done one, and would feel weird about it (don't know why). I feel I just blather on about my day and my students, and so I don't think I'd have anything to add.

7. Please don't feel weird about it-your "everyday blabbering" is in itself original, and a snippet written just for my site would liven things up and give my audience a fresh/cheerful perspective. Lol you are one adorable teacher.

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