### Debbie LloydWashington County Schools

#### Description

Help your students to follow that graph with ease. In this lesson, students investigate, analyze, and discuss the effects of parameter changes on a trigonometric function using a graphing calculator.

#### Objectives

Describes, analyzes and generalizes relationships, patterns, and functions using words, symbols, variables, tables and graphs.

Determines the impacts when changing parameters of given functions.

#### Materials

-Graphing Calculator (one for each student) or computers with graphing calculator program or access to the Internet to use the online calculator at http://coolmath.com/graphit/
-If using a computer graphing calculator software program, a presentation device for whole class projection
-Paper and colored pencils
-CD player
-Tape with song “Changes in Latitudes, Changes in Attitudes” by Jimmy Buffet
-Copies of the associated classwork file, one for each student
-Copies of the associated homework file, one for each student
-One copy of the demonstration sheet for the teacher (see associated file)

#### Preparations

1. Duplicate each student a copy of the attached files.
2. Set up the music player and the music or tape.
3. Acquire a graphing calculator for each student.
5. If using computer graphing calculator software, each computer should have the software already loaded and working properly.
6. If using the online calculator located at www.coolmath.com/graphit/ be sure all computers are able to access the Internet and the site has been bookmarked.
7. If using the computer be sure to have your presentation system set up and working properly.
8. Print out the teacher demonstration sheet to use during class discussion.

#### Procedures

1. As students enter the class, have the song “Changes in Latitude, Changes in Attitude” by Jimmy Buffet playing on the CD player or tape player.

2. Explain to the students that today, they are going to be investigating the graphs of the six trigonometric functions and will be discovering how changes in the equation of the basic function (i.e. y = sin x, y = cos x, y = tan x, y = sec x, etc.) affect the graph of the function.

3. Demonstrate how to use the overhead graphing calculator or computer graphing calculator by working with equations the student is familiar with (i.e. y = x2, y = (x + 2) 2, y = 3x2, y = -x2, etc. See the associated file). Be sure to use proper vocabulary: vertical shift, horizontal shift, etc.

4. Give each student a copy of the worksheet (see associated file). Instruct them to substitute at least three different values for each variable. Graph each different equation and sketch the graph of each using a different colored pencil. After graphing each function, they should make a conjecture as to the effect changes in this parameter make to the basic equation.

5. Have students check their conjectures with each other. After students have completed the discovery portion of the lesson, go over the effects of each parameter change and introduce the proper vocabulary (i.e. vertical shift, amplitude, phase shift, period, etc.).

6. Have students complete the homework assignment (see associated file).

#### Assessments

Students determine the effects of various parameter changes on a given trigonometric function, graph the function and use their knowledge to describe, analyze and generalize a function from it’s graph. Students will complete the homework worksheet. The teacher will check the worksheet for accuracy.