Making Waves... with pasta! (Day 2 of 2)

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Objective

SWBAT generate the graphs of sine and cosine using the unit circle and find the domain, range, and intercepts for the sine and cosine graphs.

Big Idea

Students build the sine and cosine functions using the unit circle and pasta.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

Sine (Graphs)

trigonometric functions (Graphing)

unit circle

Standards

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-IF.C.7e

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

HSF-TF.A.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

HSF-TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Building the Sine and Cosine Curves

40 minutes

Students should pick up where they left off on building their sine and cosine functions. Students should be working through the Student Handout - making waves and using the Building waves templates as an aide. See the Making Waves with pasta Day 1 lesson for more details.

This is what one of my student's work looked like as he started day 2: Sine Curve in Progress

As students completed their work I asked them to hang it around the classroom. It was helpful to have these basic parent functions displayed around the classroom as a reference when we moved into shifting sine and cosine functions and as students started to learn how to write an equation to model various trigonometric situations.

If students finish early, I encourag them to get a head start on their homework for the night.

Closure: Clicker Questions

10 minutes

In the last 10 minutes of class, I stopped my students and asked them to reflect on the four clicker questions on pages 2-5 of today’s Flipchart_ Making waves. Hopefully, students should be using their newly created graphs to identify the domain and range of the sine and cosine functions.

Homework

As students finished or at the end of class I assigned Homework 6 - Trigonometric Functions.docx to be completed this evening.

Please note: I have continued numbering these homeworks from the last unit (Rotaitons and Cyclical Functions) as the topics are closley related and my district has us teach this as one large unit. So the first homework assignment in this mini-unit will be #6.

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