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# Building the Unit Circle (Day 2 of 2)

Lesson 5 of 10

## Objective: SWBAT identify special angles in the unit circle and find the coordinates of these angles.

## Big Idea: Students use prior knowledge of circles and angles and their cut-out special triangle templates to build the unit circle.

#### Warm-up

*3 min*

To warm-up for Day 2 of Building the Unit Circle, I want to remind students of what the unit circle is: A circle with a radius of 1! So I presented them with the clicker question on page 6 of the Flipchart_Building the Unit Circle. This lesson also requires students to access their prior knowledge of writing the equation of a circle.

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#### Building the Unit Circle

*27 min*

For the majority of the class period today, my students will continue to build the unit circle on their Unit Circle Template as described in the Student Handout - Building the Unit Circle from yesterday.

Today’s focus will be on having students use their special triangle templates to generate the coordinates of the unit circle. It is very important that they have correctly built their special right triangles to have accurate side length measurements when the hypotenuse of the triangle is one and that they have copied this measurements onto both sides of the paper triangle as they will need to flip the triangle as they move into different quadrants. Here is an example of how my students will be using the triangles to create the unit circle: Day 2 building.

I will be looking to see how long students continue to use their special triangle templates before they can generalize the pattern and conclude the coordinates will be very similar in each quadrant (of course just differing in signs). I think this is a good assessment of students’ current progress with **Math Practice 7**, looking for and making use of structure, and **Math Practice 8**, looking for and expressing regularity in repeated reasoning.

I will use Question 13 to wrap up class, if I do not have time for today’s planned closure clicker questions. It is also a good question that higher level students can spend some time on while our slower moving students are still building their unit circles.

**Supplies: **Students may still need a pair of scissors to cut out the special triangles if they did not get to this yesterday.

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#### Closure: Clicker Questions

*10 min*

There are 4 clicker closure questions located on pages 7-11 of today’s Flipchart_Building the Unit Circle.pdf. It is not necessary to squeeze these questions into this lesson as students will also practice this skill of using the unit circle to determine sine and cosine values later in this unit. So if my students need more to time build the unit circle, or, to discuss the patterns in their teams I will choose to use the time for those purposes.

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Assign Homework 3 - Trigonometric Functions.docx from this unit. A homework quiz over worksheets #1-3 is planned for the next lesson.

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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