# ALEX Learning Activity

## Cutting Up With the Unit Circle

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: 2617 Title: Cutting Up With the Unit Circle Digital Tool/Resource: Cutting Up With the Unit Circle Google Doc Activity Web Address – URL: https://docs.google.com/document/d/19G6V67udBdzeQtifsBGoTcnr9tEqTM0Ya_sWnCPYcjE/edit?usp=sharing 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.
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 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

Strategies, Preparations and Variations
 Phase: During/Explore/Explain Activity: 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.The teacher will need to put the students into groups of two.  Each group will need to have the following supplies:Four copies of the Unit Circle  A copy of the student directions for each groupTwo blank 8.5’ X 14’ sheets of computer paperA fine point Sharpie or black penFour different colored highlightersScissorsDouble-sided tape (my preference-less mess) or Stick glueRulerAfter 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: 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. Advanced Preparation: The teacher would need to make enough copies for each group of the blank Unit Circle and student directions.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 Variation Tips (optional): 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. Notes or Recommendations (optional): ALCOS 2019Alg II 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.Alg II 35).  Choose trigonometric functions (sine and cosine) to model periodic phenomena with specified amplitude, frequency, and midline.
Keywords and Search Tags
 Keywords and Search Tags: cosine, radian, radian measure, reference angles, right triangles, sine, trigonometry, unit circle