# Spaghetti trig

Also it results in great discussion about the fact that the x-axis as they call it is now labeled theta and the y-axis is now measuring the x-values from the unit circle which is used to create the cosine function.

Doing this project helped me visually see how the three functions relate and work.

When I repeated this activity with my GK12 partnership teams it lead to even more great discussion about the conventions we use in our classrooms.

What I learned from teaching this lesson: For general buy-in, it is really good for students to make predictions about how they think the graph will continue past 15 degrees, at the start of the lesson.

Another idea that was presented was to have students write a sentence or two on the edge of their plot to indicate what happens as the function approaches infinity, I like this idea and will be trying it out next semester. Take another piece of spaghetti and measure the y-coordinate sin x of the point on the circle.

## Spaghetti trig

Stick it down and label the angle. Transfer this piece to lie on the trig graph vertically above the 15deg mark. It was very satisfying to show the animations found here in order to discuss the shapes of the curves. So if you're measuring cosine you start with angle 0 and measure the perpendicular length from the y-axis to the circle at angle 0 and you cut that length in spaghetti and lay it down on the graph. Also it results in great discussion about the fact that the x-axis as they call it is now labeled theta and the y-axis is now measuring the x-values from the unit circle which is used to create the cosine function. We used the length of those to construct our graphs. You then measure either the cosine or sine values that correspond with the given arc-length on the unit circle.

That string is laid down as the independent variable x-axis. When you have finished, draw a line going over the top of all your spaghetti sticks to show the graph. Transfer this piece to lie on the trig graph vertically above the 15deg mark.

This is a standard activity from the high schools my GK12 students work with but none of our undergrads had seen it. I certainly needed to demonstrate the first couple of noodles for students to get the idea, but they loved it.

## Spaghetti sine curves answers

Do not yet label the y-axis. I certainly needed to demonstrate the first couple of noodles for students to get the idea, but they loved it. Students will need: Blank unit circle and trig. Through doing this I was able to show the differences in each of the three functions. This lesson was adapted from the NCTM website. Stick it down and label the angle. Requiring the arrows on these plots especially the trig functions has helped clear some of these misunderstandings. You then measure either the cosine or sine values that correspond with the given arc-length on the unit circle. The activity We used the length of those to construct our graphs. When I repeated this activity with my GK12 partnership teams it lead to even more great discussion about the conventions we use in our classrooms.

Do not yet label the y-axis. It sounds confusing now but the hands-on interaction and group work really keep it interactive and engaging. I require all my students to add arrows to the end of their plots of continuous functions.

The activity

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