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# Discovering Trig Identities (Day 1 of 4)

Lesson 1 of 16

## Objective: SWBAT visualize and interpret the trigonometric identities with a focus today on reciprocal identities.

#### Warm-Up

*10 min*

In today's lesson it is important to take some time at the beginning of class to set the stage for students. I will talk about where we have been, where we are now, and where we are going in Trigonometry. I want students to believe that they now have a lot of knowledge from our prior units (**Trigonometry Basics** and **Trigonometric Functions**). In this unit we will pull everything together. Our first goal is to learn about Trig Identities. Later, we will apply these tools to solve equations.

Next, I will remind students what an identity is and how they are used in mathematics. I plan to have students add the definition of an identity to their notes for reference. Then, in teams, students will work on the three Warm Up problems. These problems are on Pages 3-5 of the Discovering Trig Identities Flipchart.

- Problem 1: Students are asked to text in one thing they already know about reciprocal trig functions.
- Problem 2: Students are asked to text in one thing they do not understand about reciprocal identities.
- Problem 3: Students are asked to text in one question they have about Trig Identities.

Depending on how quickly the lesson is moving, I may address some of these questions now or save them for down time later in the unit.

**Teacher's Note**: While students are responding to the warm-up prompts, I will call students up group-by-group to transfer a Ti-Navigator calculator file to their calculators.

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#### Investigation

*20 min*

For the middle part of today’s lesson, I am giving my students a calculator based assignment (see Proofs_of_Identities). I like to start this sequence of lessons off with approachable, hands-on calculator work. Building on the theme of applying existing knowledge, I provide the students with time to explore on their calculators. My goal is for my students to complete Questions #1-3 on their handout. (This content is on Pages 1.1-1.2 in their Ti-Navigator calculator file). However, I encourage students to keep working and complete as much of the investigation as they can in the time afforded to them.

The original lesson published by Texas Instruments can be found here. I provide a little more detail about how I will interact with students during this investigation in the Day 1 Middle video.

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#### Closure

*15 min*

Today’s closure to the lesson is very important!

Since this is a discovery lesson, it is important to review the learning objectives with the students at the end of the class. Hopefully, the students will indicate that they learned the intended concepts and skills when they summarize their work. But, it is important to assess the success of the lesson before the students depart.

I tell my students that if they don’t understand a problem that we discuss during today's closure, they should ask a question or ask for help. Because of this, I allocate about 15 minutes for today's closure assessment. Pages 7-13 of the Discovering Trig Identities Flipchart include the six review questions that I want my students to respond to before leaving class. To successfully answer these questions students must persevere in solving them (**MP1**) and reason abstractly (**MP2**). The last question requires students to identify the structure in the expression and work toward applying their current knowledge to simplify the expression (**MP7**). I expect about half of my students to answer this question correctly today. The data that I get from asking the question will help me to plan more well targeted lessons as we proceed with the unit.

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Today, I assigned Trig Equations Homework 1 for this unit which reviews many past concepts and has students practice simplifying basic identities.

#### 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: Discovering Trig Identities (Day 1 of 4)
- LESSON 2: Discovering Trig Identities (Day 2 of 4)
- LESSON 3: Discovering Trig Identities (Day 3 of 4)
- LESSON 4: Discovering Trig Identities (Day 4 of 4)
- LESSON 5: Simplifying Basic Trig Expressions – Connect the Dots
- LESSON 6: Verifying Trig Identities (Day 1 of 2)
- LESSON 7: Verifying Trig Identities (day 2 of 2)
- LESSON 8: Solving Basic Trigonometric Equations
- LESSON 9: Group Quiz - Solving Trig Equations
- LESSON 10: Solving Quadratic Trig Equations (Day 1 of 2)
- LESSON 11: Solving Quadratic Trig Equations (Day 2 of 2)
- LESSON 12: Puzzle - Solving Variety of Trig Equations
- LESSON 13: Sum and Difference Identities
- LESSON 14: Error Analysis - Sum and Difference Identities
- LESSON 15: 4-way Representation - Trig System of Equations
- LESSON 16: Review for test