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# Putting All of the Pieces Together

Lesson 12 of 15

## Objective: SWBAT review all of the trigonometric identities from this unit.

*50 minutes*

#### Which Identity Am I?

*15 min*

At this point students know all of the trig identities and have been using them to solve equations and figure out trig values at specific angles. Today is a chance to take a breather and to really reflect on all of these properties.

The first activity for today involves index cards, masking tape, and lots of movement and talking. Students will be given an index card that has the formula for a trig identity on it. Without looking at it, students will tape it to their forehead and will try to figure out what their expression is equivalent to.

**Teacher note:** make sure you test different kinds of tape - I find that masking tape works well and doesn't fall off easily.

The catch is that they can only ask **"yes" or "no" questions** to their classmates. Students will be able to walk around and ask one question from each student. Once they figure out what identity they have, they can come up to the front of the room and you will check it on the answer key that you have. If they get it correct, I give them the worksheet that we are doing today (attached in the next section).

I find that it usually helps to** model this game** for my students to get them thinking about good questions to ask. I always start by taping one to my forehead and asking students about it. Some example questions are given below.

- Does my expression have a square root?
- Does my expression have both sine and cosine?
- Does my expression contain tangent?
- Does my expression have more than one term?

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#### Summarize

*35 min*

This worksheet is a good **summary of many of the concepts** that we have worked on in this unit. As we are nearing the end of the unit, this is a good opportunity to focus on the big picture and to think about how these relationships work.

On the** first page of the worksheet**, students have to simplify the expression using one of the identities that they know. For example, #1 would become sin(99°) once simplified completely. I usually go through this one as an example to let students know that they may need to use two formulas (the cofunction identity and the sum formula in this case).

The **last question** instructs students to find the exact value of sin(18°). This is a challenging problem but it walks them through the process. It is a worthwhile problem because is combines so many different facets (trig identities, factoring, solving for a variable, polynomial division, and possible sine values). My students struggled to get started, but once they got through the first few steps they were on their way. It definitely helps to have them working in groups to bounce ideas off of each other.

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: Trigonometric Identities - Day 1 of 2
- LESSON 2: Trigonometric Identities - Day 2 of 2
- LESSON 3: Student Work Day and Individual Conferences
- LESSON 4: Does cos(A - B) = cos(A) - cos(B)?
- LESSON 5: If sin(A) = 3/5, what is sin(2A)?
- LESSON 6: Formative Assessment Review
- LESSON 7: Formative Assessment: Simplifying Identities and Trig Formulas
- LESSON 8: What is cos(22.5°)?
- LESSON 9: Solving Trig Equations
- LESSON 10: Using Formulas to Solve Trig Equations
- LESSON 11: Extraneous Solutions
- LESSON 12: Putting All of the Pieces Together
- LESSON 13: Formative Assessment: Solving Trig Equations
- LESSON 14: Unit Review Game: Lingo
- LESSON 15: Unit Assessment: Trigonometric Relationships