# Trigonometric Graphs Activities

Instructor: Clio Stearns

Clio has taught education courses at the college level and has a Ph.D. in curriculum and instruction.

Learning how to graph trigonometric concepts and functions is a significant part of comprehending the relationship between trigonometry and geometry. This lesson offers activities that help with teaching trigonometric graphs.

## Trigonometry and Graphing

As a high school trigonometry teacher or a teacher who incorporates trigonometry into your geometry instruction, you want your students to be able to visualize the concepts you are teaching them. Sometimes this means spending some dedicated time working on what a trigonometric graph might look like, or how to illustrate trigonometric functions and identities graphically.

Because graphing is ultimately a very visual phenomenon, teaching about trigonometric graphs offers a great opportunity for you to incorporate some activities into your instruction. This will also give your students a chance to do the hands-on learning that they will be more likely to internalize and remember.

The activities in this lesson appeal to different learning styles and strengths while helping students learn more about trigonometric graphing.

## Visual Activities

This section provides activities that are meant to work well for the visual learners in your class.

### Explaining Waves

One of the first steps to understanding trigonometric graphs is interpreting what a sine wave looks like. Have your students look at an image of a sine wave. As a class, discuss what each of the points on the wave represents and why this overall shows a sine.

Then, break students into small groups. Give each group an image of a cosine wave. Ask them to answer the following questions:

• What is similar and different between a sine wave and a cosine wave?
• Choose three different points along this wave and explain what they represent.
• Why do you think both the sine and cosine wave repeat themselves indefinitely?

### Graphing Identities

For this activity, students will work with one of the trigonometric identities. You can assign a different identity to different groups, or you can have students work through one identity at a time as a class.

In small groups, ask your students to focus on one of the major trigonometric identities. Have them create a graph using colored pencils to graph f(x) and x for the identity, including intercepts, maximum points, and minimum points.

• What is the maximum point, and how do you know? What is the minimum point, and how do you know?
• How does this graph help you understand the identity you are working with?
• What does this graph make you think about any real number x within the identity you are working with?

Give students a chance to share and discuss their graphs as well as their answers with classmates, and display their graphs around the room for future reference.

## Tactile Activities

Here, you will find activities that will support learners who like to use their hands and bodies as they deepen their understanding.

### Graph on the Ground

This kinesthetic activity will help your students find the zeroes in a trigonometric graph. Have your students help you make a large circle on the classroom floor or the ground outside using tape or chalk.

Then, ask them to walk to where they think the zeroes of a given sine are on the circle; in other words; where will the sine be equal to zero? Discuss any discrepancies that arise. Then, ask students to use chalk or tape to mark out other points on the circle that are significant when it comes to understanding the trigonometric functions.

### Building Waves

This is another activity that will further familiarize your students with how and why the sine and cosine waves work graphically. Have students work in partnerships. Each pair should begin with glue, a strip of cardboard, toothpicks, and string.

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