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# What does the unit circle tell us? (Day 2 of 2)

Lesson 7 of 10

## Objective: SWBAT use the unit circle, the Fundamental Pythagorean Identity, and right triangles, to find the values of trigonometric functions.

## Big Idea: Students extend the definitions of sine and cosine to all angles, including those representing more than one complete revolution and those that are negative.

*50 minutes*

#### Homework Quiz

*10 min*

During the first 10 minutes of class today, Students will be taking their** homework quiz **over worksheets #1-3: Homework Quiz #1-3. The clicker version of the homework quiz is located on page 6 of Flipchart_Using the Unit Circle Day 1 and 2.flipchart

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For the next part of class, students will have a few more minutes to finish yesterday’s handout, Student Handout - what does the unit circle tell us. My students struggled a bit with question 4d. I tried to lead students to the answer by having them write A, S, T, and C around the quadrants and then think about what a, b and c was asking. If I found that students were spending too much time here, I would just give them the answer. To me, it isn’t really important that they figure this mnemonic device out on their own, but rather just know how to use it.

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#### Checks for Understanding

*10 min*

After students have completed their handout from yesterday's lesson, I want to get a sense of how well students understand the evaluation of trigonometric functions for negative angles and angles that exceed 360 degrees. I also want to assess their current understanding of finding tangent values. To informally gain this information, I plan to have students answer the clicker questions on pages 7-12 of today’s flipchart: Flipchart_Using the Unit Circle Day 2.pdf (PDF pages 3-8).

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#### Summary and Closure

*15 min*

Page 13 of Flipchart_Using the Unit Circle Day 2 (Page 9 in PDF version) summarizes the key concepts from today’s learning. I encourage my students to copy these key ideas into their math notebooks as a reminder. Then, I asked students to extend their knowledge by completing the questions on Page 14 of the flipchart (PDF page 10) as a closure activity.

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I will assign Homework 4 for homework this evening. Students will also be encouraged to start memorizing the unit circle and ways to quickly evaluate the six basic trigonometric functions. I announce that we will have a quiz two class periods from now.

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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: Angles and Rotations
- LESSON 2: Investigating Radians
- LESSON 3: Radians Formalized
- LESSON 4: Building the Unit Circle (Day 1 of 2)
- LESSON 5: Building the Unit Circle (Day 2 of 2)
- LESSON 6: What does the unit circle tell us? (Day 1 of 2)
- LESSON 7: What does the unit circle tell us? (Day 2 of 2)
- LESSON 8: Periodicity and Symmetry
- LESSON 9: Unit Circle Cake Walk (and other fun Unit Circle activities!)
- LESSON 10: Group Quiz - Unit Circle Applications