Learning Activity

Closing Up the Unit Circle

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Closing Up the Unit Circle is a Google Form that has two higher-level thinking questions as a quick assessment of learning for the lesson. This form is formatted as a quiz to be used after a lesson on modeling the sine curve and right triangles.

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

After/Explain/Elaborate
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

After a lesson on the Sine Curve using right triangles, the teacher will use the Google Form, Closing Up the Unit Circle, to assess student knowledge of the lesson.

Assessment Strategies

Assessment Strategies

The teacher would assess the students by grading the Closing Up the Unit Circle quiz.

Variation Tips

A paper printout of the form could be used if the technology is limited.

When the cosine curve is being studied the teacher could modify the form questions to turn the quiz into a quiz about cosine curves.

Background and Preparation

Background / Preparation

  1. The teacher would need to ensure that there was a classroom set of Chromebooks/laptops/computers so that the students could take the quiz.
  2. The teacher would need to create a link either via email or Google Classroom to be shared with the students so that they could take the quiz.

Digital Tools / Resources

Closing Up the Unit Circle Google Form
https://docs.google.com/forms/d/1WSZIJz4K4uSDXxbv1QswjcU9zZkS0uxFCYOXNpILFzE/ed…

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