Creating the Sine and Cosine Curve

While some people are not fans of this lesson, it's my second year doing it and I like it well enough. Here is the link to the actual Illuminations lesson.

You need butcher paper, yarn, spaghetti/fettucinni, yard sticks, measuring tape, and Sharpies.

I break the project into parts. First I send students on a 'mission' to get the butcher paper. When they come back, I have supplies laid out for them. They follow the directions to create a unit circle and function graph.

They then move on to the second sheet of directions. In this section they are using a giant protractor (printed on transparencies) and a yardstick to measure increments of 15 degrees around the unit circle.

Next they wrap the yarn around the circle and mark the angles with Sharpie on the yarn. This is so they can stretch the yarn out on the function graph and transfer the angles. They then label the function graph with degrees. The fettucini is used to measure the vertical distance on the unit circle from the each angle to the x-axis. Then it is placed on the function graph where students make dots and then eventually connect into the sine curve (remind them where sine should be positive and negative, above or below the x-axis). Last they will label the x-axis with radians.

One of my favorite parts of this is printing each question separately on a post-it (each pair gets a different color).

I give them questions #1-6 on post-its. They write the answers on the post-it and tape it to their paper. I do this by first printing on regular paper. Then place post-its over each box. When you print the second time, remove the outline of the boxes to print words only on each post-it. I think it helps students not be overwhelmed by focusing on one question at a time.

After #1-6 (this also gets printed on a post-it) it's time to measure the horizontal lengths from each angle to the y-axis and create the cosine curve (they will need some prompting with this idea).

And the last four questions printed on post-its.

As each pair finishes, I give them reflection questions. I'm really proud of these. They have to analyze their graph and compare it to exact values from the unit circle and the calculator. My goal was for them to realize where the curves come from and think about what the numbers mean and I think I accomplished that.

We follow this up in our INBs with these two pages.

Here are the files:

And here are some 'live action' pictures from my class.

The final product


  1. Elissa, I used the Illuminations version this year, but I like yours better. How long did this take your kids to complete?

    1. It took my fastest group two 45 minute class period and took the rest more like 3. One group messed up and completely started over from the beginning and it took a little over 3 class periods. I definitely recommend keeping your eye on their radian measures (mine were not familiar with multiples of 15 in radians) and how they are measuring with the fettuccini.

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