## Student Activity: Solving Quadratic Trig Equations - Section 2: Student-Led Explanations

*Student Activity: Solving Quadratic Trig Equations*

# Solving Quadratic Trig Equations (Day 2 of 2)

Lesson 11 of 16

## Objective: SWBAT solve quadratic trigonometric equations.

## Big Idea: Students realize that they actually do have all the skills to solve quadratic trig equations; they just need to put the pieces together.

*55 minutes*

#### Warm-Up

*5 min*

We will begin class today by working from the Flipchart - Solving Quadratic Trig Equations. I will ask my students to solve the equation on slide 2 as a warm-up for the lesson. Hopefully, most students will be successful with this problem after yesterday’s lesson. As a form of assistance, I may post the quadratic formula as a hint/reminder for students.

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#### Student-Led Explanations

*40 min*

Today, I will breaking up this middle section of the lesson into three parts.

1. Expert Teams solve assigned Trigonometric Form from yesterday's worksheet Student Activity: Solving Quadratic Trig Equations

2. Think, Pair, Share as a team (team will solve problem, they will pair with another team, and then share thier answers)

3. Student Presentations

Here are more details on this part of the lesson: Solving Quadratic Trig Equations day 2, video narrative, working in teams

Differentiation: Today, struggling students may be supported by their teams (depending on your grouping structures). If you have students seated homogenously and you have a group or two who have been struggling with trigonometric concepts, this would be a great day to sit down with them and help clarify what they still feel is difficult for them when solving trig equations. When doing this, I always require students to ask questions. I know this is difficult for students, but they need to learn WHERE they get stuck and WHAT to ask when they have difficulties. To guide kids, I ask these questions: “Where did you get stuck?” “What do you need to know?” “How can we figure out where to get that information?”

I found most of my students had no difficulty applying the algebraic steps (completed in yesterday’s lesson) to the get down to the basic trigonometric form. However, students had difficulty actually finding the solutions for the angles that would solve the equation once in basic trig form. To help students with these issues I asked questions like: “Have you isolated for x yet?” “What is the inverse of a sine, cosine, and tangent function?” “How can you isolate x?” “How many solutions are you expecting?” “What quadrants do these answers fall in?” “How can you check your answers?” (Note: during most of the lesson students probably won’t remember to graph the equation and look at x-intercepts as we have done in the past with polynomials, but they should be comfortable with substituting the values back in for x and evaluating so that both sides are equal.)

If you have students who are advancing quickly, have them solve all the trigonometric forms, not just one.

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Following student presentations, I am going to guide students on how to quickly check their answers using a graph. I will remind students to use the ‘zoom: trig’ capability to get a nice graph with the domain of -360 degrees to 360 degrees. I am hoping this will help students to see how many solutions they should have in between 0 to 360 degrees and will help students from losing any answers.

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#### Closure - Reflections

*5 min*

To close out today’s lesson, I will ask my students to complete Section V on the Activity Sheet. In my classroom, I will leverage the personal response systems (clickers) for this task. I will ask my students to text in their answers as I display the questions on pages 4-6 of the Flipchart.

I expect my students to rate their comfort level in the 3-4 range. If students text in a 1 or 2, I will try to catch them at the end of class and ask them to sign up to come see me for help.

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Before students leave for the day I will ask students to begin working on Homework 7: Trig Equations at home this evening.

#### 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