##
* *Reflection: Continuous Assessment
What does the unit circle tell us? (Day 1 of 2) - Section 3: Closure

Many of students progressed through question one without any problems:

Correct Answer 1.jpg

Correct Answer 2.jpg

However, there were a few common errors that I observed throughout the class, particularly with parts d and e.

- Students struggling with part d, finding the equation of the circle, which lead to incorrect answers for part e: Incorrect Answer 1.jpg
- Not squaring the cosine and sine function when writing the Pythagorean identity: Incorrect Answer 2.jpg
- Missing the argument following the sine and cosine function: Incorrect Answer 3.jpg This seems to be a problem all the way through the trig units no matter how much I emphasize that trig functions must be followed by an angle or else it doesn’t make sense. Is it just laziness or a lack of understanding? I am not sure!
- Incorrect notation/squaring the angle instead of the whole function: Incorrect Answer 4.jpg

Due to the frequency and commonality of these errors, I chose to model the answer for this problem at the end of class today. Again, it will be important that students understand how the Pythagorean identity is derived in our upcoming unit.

*Continuous Assessment: Student Work (Question 1)*

# 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.

*expand content*

#### 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.

*expand content*

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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