Calculator Activity: Transformations of Trig Functions (Day 2 of 2)

1 teachers like this lesson

Objective

SWBAT identity the amplitude, period, horizontal shift, and vertical shift in the equation f(x)= a sin(bx +c)+d, and the effect that these parameters have upon the graph of the function.

Big Idea

Students use their calculators to adjust the parameters of trig functions and draw conclusions on how these parameters effect the graph.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

trigonometric functions (Graphing)

Standards

HSF-IF.C.7e

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

HSF-BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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.

MP5

Use appropriate tools strategically.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Calculator Activity: Trig Transformations

40 minutes

Horizontal Shifting with Trig Functions

Difficulties with Phase Shifting vs. Horizontal Shifting

This is a continuation of yesterday’s lesson. Students should pick up where they left off with their work on the handout Basic_Trig Transformations_Student. Today, I set the goal of having students complete the remainder of this assignment. However, if students need more time the lesson could be closed out at the start of class tomorrow. Today, students will begin to explore how to write the equation of a trigonometric function based on its graph. Students will also practice how to write cosine functions in terms of sine functions.

I choose to begin class today by reviewing question 4 as many of my students had difficulty with this yesterday. See the Horizontal Shifting with Trig Functions reflection if you want more details on how I approached helping my students with this question.

A detailed lesson plan as well as additional resources can be found as published by Texas Instrument here.

Closure: Summary and Clicker Questions

10 minutes

Once students have worked through the calculator activity, I plan to help students summarize their learning by presenting pages 4-5 of the Flipchart_Shifting Trig Functions.pdf. Using page 4, I want to insure that students understand the basic shape of the parent functions of sine and cosine.

What are some key features of these graphs?
What’s similar?
What’s different?

Then using page 5, I want to make sure that student have copied this information in their notes for future reference. After, I will have students answer the clicker questions on pages 7-11 of the flipchart if there is still time. If not, I will use these questions as a warm-up for tomorrow’s lesson.

Previous Lesson

Next Lesson