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# Puzzle - Solving Variety of Trig Equations

Lesson 12 of 16

## Objective: SWBAT solve various trigonometric equations.

## Big Idea: Students literally and figuratively put the pieces together by solving a variety of trig equations!

*55 minutes*

#### Warm-Up

*5 min*

To begin class, I ask my students to complete the warm-up on Slide 2 of Solving Trig Equations. I selected this problem so that we can review again how to either factor a trig equation or apply the quadratic formula. I want students to work independently and to get as far as they can without assistance **(****MP1**,* ***MP2)**. I ask that if students get stuck, they text me their last step.

Up to this point, my students have been successful in applying the quadratic formula to a quadratic trig equation. However, they were confused about how to interpret their solutions. After students complete the warm-up, I will model both methods. First, how to factor this polynomial to get solutions. Then, how to solve using the quadratic formula to get the values of -1/3 and 7; then, to set sine equal to these values and solve the basic trig equations from there.

The results in this problem present a good opportunity to also discuss why this equation would not produce any solutions.

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#### Closure

*10 min*

To bring closure to today’s lesson, I will have my students cut out the Trig Equations Puzzle Pieces and glue them on a separate sheet of paper. I like the idea of a puzzle instead of just a worksheet because it builds in an opportunity for review and self-assessment. **Do the pieces go together and all match? Then they are right!** I think that the visual nature of the puzzle helps kids to recognize patterns and reason about mistakes by considering alternatives.

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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