## Wednesday, January 9, 2013

### Graphing Trigonometric Functions

One unit I was really excited to teach, when I learned my classes at the beginning of the year, was Trigonometry. I had already taught it in my student teaching and had learned a few things that I would change. There are tons of ways to teach graphing trig functions but my mentor had brought a strategy to me that would have possibly been a bit easier.

Shifting X and Y Values

The way I taught my students, this semester, was extremely beneficial for all the horizontal shifts that occur in terms of period changes and horizontal/phase shifts. The way I teach my kids is to attack the graph in a few steps.

1) Graph the original function.

2) Relabel your y-coordinates by first checking for a vertical shift. This will tell you if you are "centered" around the y=0 line. If there is a vertical shift. Change this from 0 to whatever you shift is.

3) Next came the hard part. There are "two rounds" of relabeling the x-coordinates. The first round, we use the new period. This way, we have then "started" at x = 0. Relabel your end of the first cycle with the new period. I then broke this up into chunks using 1/4, 1/2, and 3/4 of the period. Do this to both sides.

4) The "second round" involves the phase shift. Add or subtract the phase shift to each of your x-coordinates. This was really hard for my kids as I learned that fractions were not their strong suits. They hated me even more as I did not allow a calculator.

That is right, I took away the calculator for graphing trig functions. MEAN MISS RUDOLPH!!!

I will say, a student told me, after he had already passed my class: "Miss Rudolph, your class and unit 5 made me much better at fractions. I actually understand them now because I was forced to learn them."

That right there, is why I loved the way I taught this.

Of course, steps 3 and 4 can be condensed once the kids have understood that you are shifting the graph by doing two rounds. Eventually, I started by making the phase shift at x=0 and then figuring out what the mark would be at the end of the cycle so I had one full period, based upon whatever this was.

I've included an image of one of the homework problems where I showed all my steps for my kids so perhaps you too can figure out what all this process was!

Pros: No Calculator!!!! Fraction Skills Improved, Learned Basic Shapes of Functions

Cons: I'm not sure everyone fully grasped what this would look like on a calculator.

What are some other ways that you teach graphing trig functions?

#### 1 comment:

1. Hello!
I taught the process similar to yours but I had them get the hardest part out of the way first. I also had them apply the transformations to the parent graph but I am not sure that this way made the most sense. Any advice please?