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Geometry Resources & Lesson Plans7 chapters | 194 lessons

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*Clio Stearns*

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.

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.

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

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 do you notice about this wave?
- 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?

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.

Then, ask them to answer these questions about their graphs:

- 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.

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

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.

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.

Start by asking them to use their toothpicks to build a plane on the cardboard, then glue a piece of string to represent the sine wave.

Next, display a different trigonometric function. Ask students to make a separate graph on their cardboard using another piece of string and representing that function graphically.

Continue until students have 'graphed' five to ten functions, then bring them together to compare.

The activities in this section will allow students to use language to deepen their understanding of trigonometric graphs.

Understanding the concept of periodicity is key to comprehending trigonometric graphs. Let students work independently for this activity. One at a time, project graphs of trigonometric functions. Students should look at the functions and then write one to two sentences describing the periodicity as quickly yet accurately as they can. After you have gone through ten functions, give students a chance to compare and contrast their descriptions.

This activity will help students understand why a tangent graph looks so different from a sine and cosine graph. Students should work with partners. Ask each pair to begin by coming up with a clear definition of tangent from a trigonometric point of view.

Then, show them a period of a tangent graph. Their task is to:

- explain why the graph looks that way, given the definition of tangent, and
- use words to describe what the full graph would look like.

When they are done, show them the full graph and see if their conjectures were accurate.

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Geometry Resources & Lesson Plans7 chapters | 194 lessons

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