Periodicity and Symmetry

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Objective

SWBAT use the unit circle to identify the periodicity and symmetry of trigonometric functions.

Big Idea

A PowerPoint presentation helps guides students to use their unit circle to better understand how sine, cosine, and tangent functions behave.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

Symmetry

Trigonometric functions

unit circle

Standards

HSF-TF.A.4

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Warm-up: Clicker Questions

5 minutes

Over the last couple of days my students ended up needing more time for the Building a Unit Circle lessons than I expected. To begin today's class, I will use some Warmup Questions that I had planned to use as Closure Questions for an earlier lesson. These questions are located on pages 6-11 of the Flipchart_Building the Unit Circle. Since the students have now learned how to use the unit circle to find sine, cosine, and tangent values, these questions serve as a review.

Explanation: Periodicity and Symmetry

45 minutes

Mathematical Practices

Periodicity and Symmetry, video narrative, mathematical practices.MP4

This section of the class is introduced using multimedia.

I used the Unit Circle Symmetry and Periodicity.ppt as a guide to walk my students through using the unit circle as a tool (Mathematical Practice 5!) to learn more about how the sine, cosine, and tangent trigonometric functions behave.
A video narrative with an overview of the PowerPoint is available here: Periodicity and Symmetry, video narrative, overview of PP.MP4