Download MAFS.912.F-TF.1 - Extend the domain of trigonometric functions

Standard 1 : Extend the domain of trigonometric
functions using the unit circle
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Algebra 2 - Additional Cluster
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.
Number: MAFS.912.F-TF.1
Title: Extend the domain of trigonometric functions
using the unit circle
Type: Cluster
Subject: Mathematics
Grade: 912
Domain: Functions: Trigonometric Functions
Related Standards
Code
MAFS.912.F-TF.1.1
MAFS.912.F-TF.1.2
MAFS.912.F-TF.1.3
MAFS.912.F-TF.1.4
Description
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle; Convert
between degrees and radians.
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.
Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the
unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x,
where x is any real number.
Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Related Resources
Image/Photograph
Name
Description
Clipart ETC: Trigonometry and
Clipart for Trigonometry and Analytic Geometry
Analytic Geometry:
Lesson Plan
Name
Exact Trigonometric Ratios:
Triangles to the Unit Circle:
Graphs from the Unit Circle
(graphing sine and cosine
curves):
Rotation Debate: Radians vs
Degrees:
Description
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 PreCalculus and Calculus.
This is a cooperative learning activity where students will convert the unit circle to a function graph. Throughout the
activity, students will correlate the two types of graphing media (unit circle vs. function graph), discover and identify
key aspects of sine and cosine wave graphs and compare their properties. The lesson includes a pre-assessment,
step-by-step instructions for the students as well as guiding questions, formative assessments and extensions for the
teachers use.
In this lesson, students will be able to answer the question why radians are the preferred measure of an angle. This
lesson nominally takes two days 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
Round and Round the Unit
This lesson discusses the Unit Circle and how to use co-terminal and/or reference angles to find any angle on the Unit
Circle:
Circle. It is an extension of trigonometric functions using the real number line.
Sine, Cosine, and Tangent:
Students will discover the connection between finding trigonometric ratios (sine, cosine, and tangent) using special right
The Leap from Special
triangles and the unit circle.
Triangles to the Unit Circle:
Spinning Angles in Radians and This lesson introduces concepts that are the prerequisites to defining trig functions on the unit circle. Radian measure
page 1 of 2 Degrees (Introductory lesson and converting between degrees and radians are introduced. Students will also learn how to draw and measure positive
to exact trigonometric values): and negative angles in standard position, identify and draw co-terminal angles, and determine a reference angle.
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 . Students will fill out a blank unit circle and provide
What is a Radian?:
themselves with their own "reference/study" guide for radian measures.
Original Tutorial
Name
Ferris Wheel Measures:
Description
By the end of this tutorial you should be able to understand the radian measures of an angle, find an angle measure
in radians given the arc length and length of the radius, and convert between degree measures and
radian measures.
Tutorial
Name
Description
This tutorial gives an introduction to the unit circle. It also extends the students knowledge of SOH CAH TOA so that
Introduction to the unit circle: they can define trigonometric functions for a broader class of angles.
Assessment
Name
Sample 1 - High School
Algebra 2 State Interim
Assessment:
Sample 2 - High School
Algebra 2 State Interim
Assessment:
Description
This is a State Interim Assessment for 9th-12th grades.
This is a State Interim Assessment for 9th-12th grades.
Student Resources
Title
Ferris Wheel Measures:
Description
By the end of this tutorial you should be able to understand the radian measures of an angle, find an angle measure
in radians given the arc length and length of the radius, and convert between degree measures and
radian measures.
This tutorial gives an introduction to the unit circle. It also extends the students knowledge of SOH CAH TOA so that
Introduction to the unit circle: they can define trigonometric functions for a broader class of angles.
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