Learning Activity

Cutting Up With the Unit Circle

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Cutting Up With the Unit Circle is a Google Doc tool that allows the student 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. The student will use reference angles on the unit circle to construct a sine curve. This allows the student to visualize where the graph originates.

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

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.

Unpacked Content

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.

Phase

During/Explore/Explain
Learning Objectives

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.

Students will be able to determine the amplitude, frequency, and midline of a trigonometric function.

Students will be able to develop a trigonometric function to model periodic phenomena

Activity Details

During a lesson on the Sine Curve using right triangles, the teacher will use the Google Doc, Cutting Up With the Unit Circle, to model the behavior of the sine curve.

Note:  If the teacher did the Before Activity,  Coloring With the Unit Circle, the reference angles will already be colored and labeled. If not, the teacher will need to use the directions from Coloring With the Unit Circle to color and label the unit circles.

  1. The teacher will need to put the students into groups of two.  
  2. Each group will need to have the following supplies:
  • Four copies of the Unit Circle  
  • A copy of the student directions for each group
  • Two blank 8.5’ X 14’ sheets of computer paper
  • A fine point Sharpie or black pen
  • Four different colored highlighters
  • Scissors
  • Double-sided tape (my preference-less mess) or Stick glue
  • Ruler
  • After the unit circles are colored, the teacher will pass out the directions for the students to follow to complete their unit circle.
  • The teacher will need to walk around the room and observe, modeling when needed.
  • Once the activity is complete the teacher will need to instruct the students in turning in their work and cleaning their work stations.
    • Assessment Strategies

    Assessment Strategies

    The teacher would assess the students by observing the  Cutting Up With the Unit Circle activity while walking around the room. 

    The teacher will also assess the students by grading the finished Cutting Up With the Unit Circle graph.

    Variation Tips

    Colored pencils could be used instead of highlighters.  

    Instead of putting the students into groups, the activity could be completed by every student.

    When the cosine curve is being studied the teacher could modify the directions to turning the triangles to the hypotenuse and allow the students to make cosine curves.

    Background and Preparation

    Background / Preparation

    1. The teacher would need to make enough copies for each group of the blank Unit Circle and student directions.
    2. The teacher will need the following supplies for each group:  

    -Four copies of the Unit Circle  

    -A copy of the student directions for each group

    -Two blank 8.5’ X 14’ sheets of computer paper

    -A fine point Sharpie or black pen

    -Four different colored highlighters

    -Scissors

    -Double-sided tape (my preference-less mess) or Stick glue

    -Ruler

    Digital Tools / Resources

    Cutting Up With the Unit Circle Google Doc Activity
    https://docs.google.com/document/d/19G6V67udBdzeQtifsBGoTcnr9tEqTM0Ya_sWnCPYcjE…

    Approved Date

    Owner (Author)

    kristylacks
    ALSDE LOGO

    This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
    Alabama Learning Exchange © 2002-2023 by Alabama State Department of Education is licensed under Attribution-NonCommercial-ShareAlike 4.0 International

    Design by Adaptive Theme