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# What does the unit circle tell us? (Day 1 of 2)

Lesson 6 of 10

## Objective: SWBAT explain how sine and cosine can be viewed in terms of the unit circle.

To warm-up for today’s lesson, I am going to have students practice the hand trick they learned at the close of yesterday’s lesson (see video below). To do this, I will ask students to quickly text in their answers to the warm-up questions on pages 2-4 of today’s flipchart, Flipchart_Using the Unit Circle Day 1. I will time these problems to encourage students to be able to quickly identify these values.

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Next, I will ask my students to begin working on the Student Handout - what does the unit circle tell us. It is possible that students may finish this work in one class period, but I am prepared to extend it over two class periods.

I expect to help many of my students with Question 1, Part d. I will remind them of the standard form of a circle, if necessary. I like observing my students working on Question 1. My students always need more practice with writing expression or equations “in terms of” a specific variable or function. In this task I can informally assess their progress. Question 3 introduces students to the fact that the tangent function is equal to the sine function divided by the cosine function.

Today, students should finish a majority of this packet. I plan to give students about 15 minutes in tomorrow's lesson to finish what they have not yet completed.

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#### Closure

*3 min*

In the last few minutes of today's lesson, I will review the answers to Question 1 with my students. I often have a few students who really struggle with this section. Even some students who think they get, use some incorrect notation. I thought it was important for students to see how they could derive the Fundamental Pythagorean Identity. Although we won't be using the identity until our next unit it is good for students to start becoming familiar with it.

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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