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# Graphing Trigonometric Functions

Lesson 5 of 15

## Objective: SWBAT graph trigonometric (sine and cosine) functions by hand.

## Big Idea: Students will apply their prior knowledge of shifting functions or the 5-point method to graph trigonometric functions.

*50 minutes*

If I was not able to wrap up the calculator activity during yesterday’s lesson, I will have students complete the clicker questions as a warm-up today. The summary clicker questions for shifting trigonometric functions are located on pages 7-11 of the Flipchart_Shifting Trig Functions.flipchart. I think it is important for students to have a solid understanding of how parameter changes on an equation affect the graph of trigonometric equation to aide in their ability to graph the functions by hand. I find that some of my students will use this method to graph trig functions and others will use it to check their graphed equations for accuracy.

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In the middle part of today’s lesson, I plan to model for students a few different methods to graph trigonometric functions by hand. I think the most consistent and accurate method is to use the 5 Point Method. I am going to teach this as the primary method for graphing, but I will also show my students some other methods that will help them to check their work.

Every student will get a Graphing Trig Functions by hand handout. I want to scaffold their note taking as I model a few problems. Nonetheless, I want my students to take notes in their own words, to describe the steps of the 5-point method in their own language as we work together.

Once we have practiced the 5-point method, I will review the concept of shifting and have students check their answers by using their shifting knowledge. Also, I want to model for students the idea of a making a T table to graph trig functions (using angle inputs, find the output, plot the point). I find that students really like this method, but I caution them against using only this method because they need to be assured that they are picking the correct inputs to get a good representation of the graph. So, I really try to push my students to only check their answers using this method.

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#### Closure: Practice Problems

*10 min*

For the last few minutes of class, I want students to practice graphing trig functions by hand. I will have them complete the last two problems on their Graphing Trig Functions by hand handout for today working independently. Then, I will review answers with the class before the students leave for the day.

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Making Waves... with pasta! (Day 1 of 2)
- LESSON 2: Making Waves... with pasta! (Day 2 of 2)
- LESSON 3: Calculator Activity: Transformations of Trig Functions (Day 1 of 2)
- LESSON 4: Calculator Activity: Transformations of Trig Functions (Day 2 of 2)
- LESSON 5: Graphing Trigonometric Functions
- LESSON 6: One of Those Days
- LESSON 7: Modeling Using Trig Functions
- LESSON 8: Modeling Real World Data (Day 1 of 4)
- LESSON 9: Modeling Real World Data (Day 2 of 4)
- LESSON 10: Modeling Real World Data (Day 3 of 4)
- LESSON 11: Modeling Real World Data (Day 4 of 4)
- LESSON 12: Trig Millionaire Game
- LESSON 13: More Trig Functions
- LESSON 14: Trigonometric Functions Review
- LESSON 15: Trigonometric Functions Unit Assessment