ALEX Learning Activity

  

Unit Circle: Exploring Unit Circle Trigonometry With Desmos

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

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  This learning activity provided by:  
Author: Kristy Lacks
System:Marshall County
School:Douglas High School
  General Activity Information  
Activity ID: 2605
Title:
Unit Circle: Exploring Unit Circle Trigonometry With Desmos
Digital Tool/Resource:
Desmos Trigonometry: Unit Circle Application
Web Address – URL:
Overview:

Desmos is a free online graphing calculator that has several mathematical applications that can be used in the classroom. The Trigonometry: Unit Circle Application is a tool that can be used to study the Unit Circle and the different parts that make up the Unit Circle such as reference angles, radian measure, trigonometric ratios, and angle measurements.

This resource was created as a result of the ALEX Resource Development Summit.

  Associated Standards and Objectives  
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
37 ) Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [F-TF1]

Mathematics
MA2015 (2016)
Grade: 9-12
Algebra II with Trigonometry
38 ) 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. [F-TF2]

Learning Objectives:

Students will use radian measure as a ratio of the arc length to the radius.

Students will be able to accurately find relationships of trigonometric functions for an acute angle of a right triangle to measure within the unit circle.

Students will be able to justify triangle similarity.

Students will be able to find the reference angle for any angle found by a revolution on a ray in the coordinate plane.

Students will be able to relate the trigonometric ratios for the reference angle to those of the original angle.

Students will be able to determine the appropriate sign for trigonometric functions of angles of any given size.

  Strategies, Preparations and Variations  
Phase:
Before/Engage
Activity:

  1. Distribute the Chromebooks/laptops to the class under your normal distribution procedures.
  2. Pass out the Unit Circle with Desmos directions to each student.
  3. Model on the projector/interactive whiteboard/panel display how to get to the website using the directions that you distributed.
  4. Talk about each of the formula bars represented in the Desmos Trigonometry: Unit Circle Application.  
  5. Explain that the “formula 2” is a point. Talk about what the coordinates are.
  6. Ask the students, “Why would this point, (cos a, sin a),  be important to show on the Unit Circle?”
  7. Lead students to talk about the trigonometric ratios and reference angles. Be sure to demonstrate using the online application to model for the students.
  8. Discuss the triangle similarities around the Unit Circle. Be sure to demonstrate using the online application to model for the students.
  9. Talk about the ratio of the arc length to the radius of the circle. Be sure to demonstrate using the online application to model for the students.
  10. Talk about the signs in each quadrant.  Be sure to demonstrate using the online application to model for the students.
  11. Demonstrate the “a” value at different points around the circle.
  12. The teacher would want to give the students just enough knowledge to create curiosity about the subject matter.
  13. Allow the students to explore the activity for 2-3 minutes. Stress to the students that this time is for them to explore what the application demonstrates and come up with ideas of why the various functions work the way that they do.
  14. Go around the room watching the students as they are exploring the application.
  15. After the 2-3 minutes are up, instruct the students to do number 4 on their directions.
  16. Collect student responses on paper.
  17. Go through the answers and select answers that reflect ideas that would build student knowledge, display them on the board, and discuss with the class.
Assessment Strategies:

The teacher would assess the students by walking around the room observing what the students are doing with their graphs.

The teacher will also assess student understanding by reading and displaying the student answers to the question given.


Advanced Preparation:

  1. The teacher would need to make copies of the Unit Circle with Desmos to hand out to students.
  2. If the teacher has no prior knowledge of Desmos, the teacher would need to gain a working knowledge of the Desmos Graphing Calculator before this lesson.  
  3. The teacher would need to make sure a classroom set of Chromebooks or laptops were available for this lesson.
  4. A timer of some kind will be needed for this lesson.
Variation Tips (optional):

The teacher could assign the Unit Circle with Desmos Directions to the students via Google Classroom or another online learning management system instead of having paper copies. If the teacher chooses to do this, the teacher could pass out index cards for the students to answer the question.

This same activity can be used as an after activity. If doing this, I would suggest creating more questions to answer so that each objective in the lesson is covered.

Notes or Recommendations (optional):

ALCOS 2019

Alg 2 3-21.  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, building on work with non-right triangle trigonometry.

1-34.  Define the radian measure of an angle as the constant of proportionality of the length of an arc it intercepts to the radius of the circle; in particular, it is the length of the arc intercepted on the unit circle.

  Keywords and Search Tags  
Keywords and Search Tags: cosine, desmos, radian, radian measure, reference angles, right triangles, sine, trigonometry, unit circle