# Cluster 1: Extend the domain of trigonometric functions using the unit circle. (Algebra 2 - Additional Cluster)Archived Export Print

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

General Information
Number: MAFS.912.F-TF.1
Title: Extend the domain of trigonometric functions using the unit circle. (Algebra 2 - Additional Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Functions: Trigonometric Functions

## Related Standards

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MAFS.912.F-TF.1.AP.1a
MAFS.912.F-TF.1.AP.1b
MAFS.912.F-TF.1.AP.2a
Label the unit circle.
MAFS.912.F-TF.1.AP.2b
Use the unit circle to label ordered pairs for cosine and sine.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

## Image/Photograph

Clipart ETC: Trigonometry and Analytic Geometry:

Clipart for Trigonometry and Analytic Geometry

Type: Image/Photograph

## Lesson Plans

Sine, Cosine, and Tangent: The Leap from Special Triangles to the Unit Circle:

Students will discover the connection between finding trigonometric ratios (sine, cosine, and tangent) using special right triangles and the unit circle.

Type: Lesson Plan

Round and Round the Unit Circle:

This lesson discusses the Unit Circle and how to use co-terminal and/or reference angles to find angles on the Unit Circle. It is an extension of trigonometric functions using the real number line.

Type: Lesson Plan

Students participate in an activity that allows them to see physically and visually what a radian is. The lesson continues with the connection of radians and numbers expressed in terms of $\mathrm{p}$. Students will fill out a blank unit circle and provide themselves with their own "reference/study" guide for radian measures.

Type: Lesson Plan

In this lesson, students will convert from degrees to radians and radians to degrees and calculate arc length using both degrees and radians. Students will come to consensus as to why radians are the preferred measure of an angle. This lesson normally takes two 50 minute class periods to teach.

• Day 1: Bell Ringer-Day 1, Lesson Notes, Activity 1
• Day 2: Day 1 Review and Wrap-up, Bell Ringer-Day 2, Activity 2

Type: Lesson Plan

Spinning Angles in Radians and Degrees (Introductory lesson to exact trigonometric values):

This lesson introduces concepts that are the prerequisites to defining trig functions on the unit circle. Radian measure and converting between degrees and radians are introduced. Students will also learn how to draw and measure positive and negative angles in standard position, identify and draw co-terminal angles, and determine a reference angle.

Type: Lesson Plan

Exact Trigonometric Ratios: Triangles to the Unit Circle:

This is a lesson in which the student learns and practices exact trig values. They are explained using triangles, then the unit circle, and then guided practice to be sure these concepts are mastered since they will be used in future problems in Pre-calculus and Calculus.

Type: Lesson Plan

## Original Student Tutorial

Ferris Wheel Measures:

Learn about the radian measures of an angle, finding an angle measure in radians given the arc length and length of the radius, and converting between degree measures and radian measures in this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

Introduction to the unit circle:

This tutorial gives an introduction to the unit circle. It also extends the students knowledge of SOH CAH TOA so that they can define trigonometric functions for a broader class of angles.

Type: Tutorial

## Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

## Original Student Tutorial

Ferris Wheel Measures:

Learn about the radian measures of an angle, finding an angle measure in radians given the arc length and length of the radius, and converting between degree measures and radian measures in this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

Introduction to the unit circle:

This tutorial gives an introduction to the unit circle. It also extends the students knowledge of SOH CAH TOA so that they can define trigonometric functions for a broader class of angles.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.