Unit Circle: Unit Circle with Everything by CalcWorkshop

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

CalcWorkshop is a subscription-based service, however, Unit Circle With Everything is a free webpage with printable PDFs. Unit Circle With Everything 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 activity was created as a result of the ALEX Resource Development Summit.

Phase

During/Explore/Explain
Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.21

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.

UP:MA19.A2.21

Vocabulary

  • Unit circle
  • Radian measure
  • Quadrantal
  • Traversed

Knowledge

Students know:
  • Trigonometric ratios for right triangles.
  • The appropriate sign for coordinate values in each quadrant of a coordinate graph.

Skills

Students are able to:
  • Accurately find relationships of trigonometric functions for an acute angle of a right triangle to measures within the unit circle.
  • Justify triangle similarity.
  • Find the reference angle for any angle found by a revolution on a ray in the coordinate plane.
  • Relate the trigonometric ratios for the reference angle to those of the original angle.
  • Determine the appropriate sign for trigonometric functions of angles of any given size.

Understanding

Students understand that:
  • Trigonometric functions may be extended to all real numbers from being defined only for acute angles in right triangles by using the unit circle, reflections, and logical reasoning.

Learning Objectives

Students will use the definition of one radian is the measure of the central angle of a unit circle which subtends (cuts off) an arc of length one to determine measures of other central angles as a fraction of a complete revolution (2π for the unit circle).

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.

Activity Details

  1. Pass out the How to Memorize the Unit Circle, Left-Hand Trick, and Unit Circle Chart handouts to each student.
  2. Go to the Unit Circle with Everything webpage. Scroll down to the video.
  3. Play the video from the Unit Circle with Everything webpage starting at 15:23. You will stop the video at 46:35.
  4. Have the students watch the video segment: 15:23-46:35. Tell them to take notes to encourage full participation.
  5. When the video segment is finished, go over the How to Memorize the Unit Circle, Left-Hand Trick, and Unit Circle Chart with the students to make sure to reinforce the video segment.

Assessment Strategies

The teacher would assess the students by verbal feedback given as the How to Memorize the Unit Circle, Left-Hand Trick, and Unit Circle Chart are reinforced.

Variation Tips

The teacher could distribute the handouts to the students via Google Classroom instead of having paper copies. 

Different parts of the video could be used to demonstrate different topics related to the Unit Circle.

Background / Preparation

  1. For teacher convenience, a copy of directions and links can be found on the Unit Circle- Calc Workshop document.
  2. The teacher would need to make copies of the How to Memorize the Unit Circle, Left-Hand Trick, and Unit Circle Chart handouts for each student.
  3. Prior to class, the teacher would need to check the video link to make sure that the video and sound play clearly when displayed.
Unit Circle With Everything
https://calcworkshop.com/radian-measure/unit-circle/

Approved Date

Owner (Author)

kristylacks
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