# 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: https://www.desmos.com/calculator/qmzx2skkzy 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