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

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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.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

Trigonometric functions

unit circle

Standards

HSF-TF.A.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

HSF-TF.A.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

HSF-TF.C.8

Prove the Pythagorean identity sin<sup>2</sup>(θ) + cos<sup>2</sup>(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Homework Quiz

10 minutes

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

Unit Circle Application Continued

15 minutes

Various approaches! I want more details next time!

What does the Unit Circle Tell Us, presentation of student approaches.MP4

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.

Checks for Understanding

10 minutes

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).

Summary and Closure

15 minutes

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.

Homework

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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