UNIT 2
ALGEBRA II
TEMPLATE CREATED BY
REGION 1 ESA
UNIT 2
Algebra II Math Tool Unit 2
Algebra II Unit 2 Overview: Trigonometric Functions
Building on their previous work with functions, and on their work with trigonometric ratios and circles in Geometry,
students now use the coordinate plane to extend trigonometry to model periodic phenomena.
Note:
It is important to note that the units (or critical areas) are intended to convey coherent groupings of content. The clusters and standards within units are ordered
as they are in the Common Core State Standards, and are not intended to convey an instructional order. Considerations regarding constraints, extensions, and
connections are found in the instructional notes. The instructional notes are a critical attribute of the courses and should not be overlooked. For example, one
will see that standards such as A.CED.1 and A.CED.2 are repeated in multiple courses, yet their emphases change from one course to the next. These changes are
seen only in the instructional notes, making the notes an indispensable component of the pathways.
(All instructional notes/suggestions will be found in italics throughout this document)
Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for
Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol
Template created by Region 1 ESA
Page 2 of 8
Algebra II Math Tool Unit 2
Unit 2: Trigonometric
Functions- F.TF.1
Cluster: Extend the domain of trigonometric functions using the unit circle.
Standard
Instructional Notes: none

F.TF.1 Understand radian measure of an angle as the length of
the arc on the unit circle subtended by the angle.
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Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can define unit, circle, central angle, and
intercepted arc.
I can define the radian measure of an angle.
I can extend the definition of radian
measure to show that an angle measure of
one radian occurs when the length of the
arc and the radius of the circle are the
same.
I can use a similarity approach to find the
radian measure of central angles in circles
that are not unit circles.
Essential Questions/ Enduring Understandings
When does a function best model a
situation?
Trigonometric functions are useful for
modeling periodic phenomena.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard
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Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Radian, central angle, intercepted arc, length, unit circle
Page 3 of 8
Algebra II Math Tool Unit 2
Unit 2: Trigonometric
Functions- F.TF.2
Cluster: Extend the domain of trigonometric functions using the unit circle.
Standard
Instructional Notes: none
F.TF.2 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.
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



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Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can define a radian and unit circle.
I can label the unit circle in radians since it
is known that one revolution of the unit
circle is equal to 2𝜋 radians.
I can draw central angles of given radian
measures on the unit circle with the vertex
at the origin and the initial ray on the
positive x-axis.
I can recall that in the unit circle, the cosine
of an angle is defined to be the xcoordinate where the terminal ray of angle
crosses the unit circle.
Essential Questions/ Enduring Understandings
When does a function best model a
situation?
Trigonometric functions are useful for
modeling periodic phenomena.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Radian, unit circle, co-terminal angle, output, evaluate, trigonometric function
Page 4 of 8
Algebra II Math Tool Unit 2
Unit 2: Trigonometric
Functions- F.TF.2 continued
Cluster: Extend the domain of trigonometric functions using the unit circle.
Standard
Instructional Notes: none
F.TF.2 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.












Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can recall that on the unit circle, the sine of an
angle is defined to be the y-coordinate where
the terminal ray of angle crosses the unit circle.
I can identify the cosine and sine of an angle
when given a graph of the unit circle with the
coordinates labeled.
I can explain why the right triangle definitions of
cosine and sine do not allow cosines and sines
to have negative values.
I can explain why the unit circle definitions of
cosine and sine allow cosine and sines to have
negative values.
Essential Questions/ Enduring Understandings
When does a function best model a
situation?
Trigonometric functions are useful for
modeling periodic phenomena.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Radian, unit circle, co-terminal angle, output, evaluate, trigonometric function
Page 5 of 8
Algebra II Math Tool Unit 2
Unit 2: Trigonometric
Functions- F.TF.2 continued
Cluster: Extend the domain of trigonometric functions using the unit circle.
Standard
Instructional Notes: none
F.TF.2 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.








Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets



I can define co-terminal angles.
I can identify many co-terminal angles
when given a radian measure.
I can explain why co-terminal angles will all
produce the same output when evaluated
as the inputs of a trigonometric function.
Essential Questions/ Enduring Understandings
When does a function best model a
situation?
Trigonometric functions are useful for
modeling periodic phenomena.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Radian, unit circle, co-terminal angle, output, evaluate, trigonometric function
Page 6 of 8
Algebra II Math Tool Unit 2
Functions- F.TF.5
Cluster: Model periodic phenomena with trigonometric functions.
Unit 2: Trigonometric
Standard
Instructional Notes: none

F.TF.5 Choose trigonometric functions to model periodic
phenomena with specified amplitude, frequency, and
midline.

★










Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can define amplitude, frequency, and
midline of a trigonometric function.
I can explain the connection between
frequency and period.
I can recognize real-world situations that
can be modeled with a periodic function by
identifying the amplitude, frequency (or
period), and midline.
I can write a function notation for the
trigonometric function that models a
problem situation, given the amplitude,
frequency (or period), and midline of a
periodic situation.
Essential Questions/ Enduring Understandings
When does a function best model a
situation?
Trigonometric functions are useful for
modeling periodic phenomena.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Amplitude, frequency, midline, trigonometric function, periodic function
Page 7 of 8
Algebra II Math Tool Unit 2
Unit 2: Trigonometric
Functions- F.TF.8
Cluster: Prove and apply trigonometric identities.
Standard
Instructional Notes: An Algebra II course with an additional focus on

trigonometry could include the (+) standard F.TF.9: Prove the addition
and subtraction formulas for sine, cosine, and tangent and use them
to solve problems. This could be limited to acute angles in Algebra II.
F.TF.8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and
use it to find sin (θ), cos (θ), or tan (θ), given sin (θ), cos (θ), or
tan (θ), and the quadrant of the angle.










Standards of Mathematical Practice (SMP’s)
#1 Make sense of problems and persevere in solving them.
#2 Reason abstractly and quantitatively.
#3 Construct viable arguments and critique the reasoning
of others.
#4 Model with mathematics
#5 Use appropriate tools strategically.
#6 Attend to precision.
#7 Look for and make use of structure
#8 Look for and express regularity in repeated reasoning.
Template created by Region 1 ESA
Directly
Somewhat
Not
Aligned
Aligned
Aligned
Content/Skills Included in Textbook
(Include page numbers and comments)
Suggested Learning Targets
I can derive the Pythagorean identity
sin2 (Ѳ) + cos2 (Ѳ) = 1 by using the unit circle
definitions of cosine and sine and applying
the Pythagorean Theorem.
I can use the Pythagorean identity
sin2 (Ѳ) + cos2 (Ѳ) = 1 to calculate the value
of sin(Ѳ) or cos (Ѳ) when I am given sin (Ѳ)
or cos (Ѳ) and the quadrant of Ѳ.
I can use the quotient identity
(tan (Ѳ) = sin Ѳ/cos Ѳ ) to calculate tan (Ѳ).
Essential Questions/ Enduring Understandings
When does a function best model a
situation?
Trigonometric functions are useful for
modeling periodic phenomena.
Assessment
Assessments align to suggested learning targets.
Directly
Aligned
Somewhat
Aligned
Not
Aligned
Check all assessment types that address this standard





Drill and practice
Multiple choice
Short answer (written)
Performance (verbal explanation)
Product / Project
Vocabulary
Pythagorean identity Pythagorean Theorem, unit circle, sine, cosine, tangent, quotient identity
Page 8 of 8