SWBAT generate the graphs of sine and cosine using the unit circle and find the domain, range, and intercepts for the sine and cosine graphs.

Students build the sine and cosine functions using the unit circle and pasta.

15 minutes

During yesterday’s lesson, Unit Circle Cake Walk, I may have decided to give my students an extra day to study their unit circles depending on how comfortable they were with the games. If I decided to delay the Unit Circle Quiz I would now give it at the start of class.

35 minutes

Today’s lesson requires quite a bit of Supplies. Each student will need:

- 2 handouts (Student Handout - making waves.docx and the Building waves templates.pdf)
- Can with a 3-inch diameter (this could be shared in teams)
- Glue stick
- Scissors
- Fettuccini or some other flat pasta
- Writing utensil

Students will begin building the graphs of the sine and cosine functions by following the directions outlined in the Student Handout - making waves. I love how this lesson guides students to use their prior knowledge of the unit circle to derive these functions.

First, students will need to make a paper strip with markings equivalent to the radian measures along the unit circle provided in the template (this is why it’s important the cans have a 3-inch diameter).

Here is what the process ended up looking like with my students:

Step 1: Students Set-up and Starting to Measure

Step 2: Making the Strip

Step 3: Completed Strip

Students will then use this paper strip to mark the radian measurements along their x-axis of the two graphing templates. It is important that they use this strip to keep accurate spacing between the angle markings. Finally students will use the sine lengths (or length from the x-axis to the unit circle) taken from the unit circle template to measure and break a piece of the fettuccine. They will then glue this piece onto their graph to make the sine curve. Like so...

Next students will make the cosine function using the lengths from the y-axis to the unit circle. Like so…

**Teaching Tips:**

My students seemed to find it easier to cut the fettuccini with scissors rather than break it. When they tried to break the pieces they weren’t very accurate. Also, watch out for the common mistake of students not accounting for negative values. If the sine or cosine value is negative the fettuccini piece should be placed BELOW the x-axis to account for this negative value. I also found that my students were frequently skipping the angle values of 0, pi/2, pi, 3pi/2. So I asked them to go back and do those before they connected the ‘skeleton’ of the graphs with a smooth curve.

**Pacing this lesson:**

My students pacing on this activity was quite varied. Some finished at least one graph in the first class period while others were still working on making the axes. I extended this activity into a second day as a majority of my students needed it.

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