Introduction to Sinusoidal Graphs

Ever since I started teaching PreCalculus 10+ years ago I have used Ferris wheels to introduce sinusoidal functions. Well not real Ferris wheels, although that would be really cool. But the idea of them. And we do have a little discussion about Ferris wheels in general and it's interesting to see that there are a handful of students who just don't like them. huh.

Anyhow - way back when I started teaching PreCalculus I found in this book Functions Modeling Change (but an earlier edition) the Ferris Wheel approach. Very cool. 

So I start off the discussion with a few PowerPoint slides. The one you see above is projected as students come in. Then we use ...

I actually went on the London Eye about 5 years ago. Very cool. And sometimes I have a student in my class who has been too.

Then I tell the class - okay make a graph of the height of a person on the Ferris wheel with respect to the time (in this case minutes). They work in their small groups and come up with nice sinusoidal graph. Wish I had taken pictures from my whiteboards of what they came up with. 

From here we have a discussion of periodic and sinusoidal graphs. We define those terms. we talk about characteristics and students work with more Ferris wheel scenarios. We look at some variations in the location and the height of the loading platform. Of course times and diameters change too. It's a great way to get students to think sinusoidally, relating to something they have experience with.

We use this foldable in our ISNs for periodic functions:

The four doors on the bottom two-thirds of the foldable open up:

After students do a bunch together (we have 82 minute blocks) we summarize with this example on an ISN foldable. I have students do the front and the second inside page.

The next class we focus on finding the height at certain times. This can be very confusing and difficult for students but I like how it pulls in the circle and some trig (we stay in radians). We usually end up doing a whole block of problems I make up for various Ferris wheels.

All this preliminary work gets students ready to work with the more abstract and general sine and cosine graphs.

All my graphing trig functions files are HERE (everything - a bunch of lesson materials, ISN materials, etc).