## November 15, 2015

### Sine and Cosine Waves with Activity Builder

My PreCalc students have been studying the graphs and equations of sine and cosine for a month (an interrupted month but a month nonetheless). Tuesday they will have one final day to review before their test on Thursday (we run an alternating day block schedule). Some students are completely ready. They can identify transformations, graph complex equations, and write equations from both graphs and descriptions. They can apply their knowledge to a novel context (we did a Ferris wheel project). Other students still have to think about what the graph of y=sin(x) looks like. This is the widest range of students I've ever had in an Honors PreCalculus course so I'm really appreciative that Desmos made the activity builder just in time for this class! It's a great way for me to differentiate.

Last week while working on the Ferris wheel project when I had some students who had no idea how to write an equation given their more complicated graph, I sent them to Rachel's activity builder Curve Fitting w/ Sine and Cosine that went back to the basics of equation writing. They wrote the equation for a graph with amplitude not equal to one, then I referred them back to their Ferris wheel to identify the amplitude and put it into their equation. It was great because it was self checking and students experienced some success working simpler problems when they were frustrated with the complex problem I'd posed.

Tuesday I want to create a similar situation - so I built a couple different activities.

Graphing Basic Trig Equations
This starts all the way back with y=sin(x) so my students who are lost can start back at the beginning and practice the whole unit all over again. When we sketch a graph, students plot the important points and then fill in the curve. I recreated this activity on Desmos by having students drag points on a grid. Then they can check their work by un-hiding the curve.

Sine and Cosine Graphs with Multiple Transformations
Students will describe, graph and write equations for functions with multiple transformations. This one is aligned with what will be on the test.

I would love feedback on these activities! (Especially if you can provide it before 7:24 am on Tuesday.) I'll let you know how they go after that.

#### 2 comments:

1. These look cool!

For the dragging the points, did you have a certain number of points that you wanted them to do?

I haven't built any Desmos activities yet so please forgive me if this question is ignorant--when they "send answer to a teacher" what do you do with them afterward? Would you address common mistakes with the students individually, or with the class? Also, for the equations from graph--would you want them in both sine and cosine, or either?

1. We usually do 5 points to make one complete wave. For sine it's midline, max, midline, min, midline.

In other activities analyzing common misconceptions would be a great feature but since I designed this as a review activity they get to check their work on the next slide by writing or graphing the equation so I probably won't do anything with it.

We've done some practice writing the equation using both sine and cosine but I decided not to require both for this activity. It's certainly an additional instruction you could give to a class.