Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
Enduring understanding (Big Idea): Students will be able to identify, define, and use trigonometric functions to find unknown
measures, including area, in right and non-right triangles. They will also be able to graph trigonometric parent and complex functions,
identifying amplitude, period, and midline.
Essential Questions:
 How are trigonometric ratios for acute angles defined?
 What is the relationship between sine and cosine of complementary angles and how is this relationship used to solve
problems?
 How is the Pythagorean Theorem used to solve right triangles in applied problems?
1
 How does the construction of an auxiliary line help derive the formula 𝐴 = 𝑎𝑏 sin(𝐶) for the area of a triangle?
2
 How are the Laws of Sine and Cosine used/applied to find unknown measurements in non-right triangles?
 How are geometric shapes, measures, and properties used to describe everyday objects?
 What are the graphs of the sine and cosine functions? How do you find the midline, amplitude, and period?
BY THE END OF THIS UNIT:
Students will know…
 The Sine, Cosine, and Tangent Trigonometric Ratios and
Graphs
 Law of Sines and Law of Cosines
 Graphs of Sine and Cosine
Vocabulary:
Sine, Cosine, Tangent, Auxiliary Line, Inverse function,
Opposite Side, Adjacent Side, Hypotenuse (Soh-Cah-Toa),
Period, Midline, Amplitude
Unit Resources:
Learning Task:
 CB – Exploring Trigonometric Ratios (pg. 506 in student
textbook)
 CC – 4: Complementary Angles and Trigonometric
Ratios (online and in textbook)
Performance Task:
 Task #1 - Attached
 Task #2 – Attached (Do not assign #4 on this document)
Project:
 At the website below, view #2 Trigonometry Project
http://www.freewebs.com/matheng/geometryprojects.htm
Prior Course Knowledge:
Pythagorean Theorem was introduced in 8th grade math. For
this course, we are focusing on its application in applied right
triangle problems.
Test Specification Weights for the
Common Exams in Common Core Math II:
Standard
% Constructed
Response
G.SRT
3% - 7%
G.MG
3% - 7%
% MultipleChoice
16% to 19%
Category
Percentage
(Geometry)
27% to 30%
Students will be able to:
 Use trigonometry to find unknown values in right and nonright triangles
1
 Derive and use the formula 𝐴 = 2 𝑎𝑏 sin(𝐶)to find the area
of a triangle.
 Describe everyday objects in terms of geometric shapes
 Use the Pythagorean Theorem to solve applied problems
 Interpret data to graph sine and cosine functions, identifying
period, midline, and amplitude
Mathematical Practices in Focus:
1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
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
Pearson Abbreviation Key:
CC – Common Core Additional Lessons found in the Pearson online materials.
CB- Concept Bytes found in between lessons in the Pearson textbook.
ER – Enrichment worksheets found in teacher resources per chapter.
Common Core Objectives for this unit:
G.SRT.6 – G.SRT.9, G.SRT.11, G.MG.1, F.IF.4, F.IF.7, A.CED.2
Suggested Order/Pacing with Text Resources:
Trigonometry

CC – 4

CB: Exploring Trig ratios (section 8.2/8.3)
Angle of Elevation & Depression

CB: Measuring from Afar (section 8.3/8.4)
Law of Sines& Law of Cosines

CC – 5

CC – 6
Graphing Sine and Cosine Functions

CB 13.4 Graphing Trig Functions
Modeling

This should be done throughout the entire course
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 1
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title: Right Triangle Trigonometry and Pythagorean Theorem
Standard: G-SRT.6 – Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
Concepts and Skills to Master:
 Define trigonometric ratios for acute angles
 Set up trigonometric ratios for various triangles using the given angle
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Order of operations / solving proportions
 Be able to identify the hypotenuse of a right triangle
 Be able to identify which side is opposite of a specific angle
Academic Vocabulary:
Similar Triangles, Sine, Cosine, Tangent, Opposite Side, Adjacent Side, Hypotenuse, Inverse Function
Starting Resources:
Suggested Instructional Strategies:
a) Geometry Textbook Correlation:
 This standard should be taught in conjunction with
o 8.3 Trigonometry
others in this cluster (G-SRT.7 and G-SRT.8)
i. CB – Exploring Trigonometric Ratios
 Use a mnemonic device to help students remember trig
ii. CC – 4
functions (ex. SOH-CAH-TOA)
b) Pearson Geometry Textbook Online Resources
i. Find the Errors 8.3
NCDPI Unpacking:
ii. Activities, Games, and Puzzles 8.3
What does this standard mean that a student will know and
c) “Trigonometric Functions” Activity – Omit #3 unless
be able to do?
students have already taken Algebra 2.
 Use similarity to understand and develop trigonometric
http://map.mathshell.org/materials/download.php?fileid=846
ratios for acute angles
 Set up trigonometric ratios for acute angles in right
Bank of G.SRT.6 specific resources:
triangles
http://ccssmath.org/?page_id=2283
Sample Assessment Tasks
Skill-based task:
1. Find the following ratios.
a. Sin S
b. Cos S
c. Tan S
d. Sin R
e. Cos R
f. Tan R
Problem Task:
1. If sin A = 3/5, and cos A < 0, find tan A. (from “Trigonometric
Functions” Activity listed in the resources)
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 2
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title:Right Triangle Trigonometry and Pythagorean Theorem
Standard: G-SRT.7Explain and use the relationship between the sine and cosine of complementary angles
Concepts and Skills to Master:
 Set up trigonometric ratios for right triangles
 Use these trigonometric ratios to find angle measures and side lengths
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Order of operations / solving proportions
 Be able to identify the hypotenuse of a right triangle
 Be able to identify which side is opposite of a specific angle
Academic Vocabulary:
Sine, Cosine, Tangent, Hypotenuse, Opposite, Adjacent, Inverse Function
Suggested Instructional Strategies:
Starting Resources:
a) Geometry Textbook Correlation:
This standard should be taught in conjunction with others
o 8.3 Trigonometry
in this cluster (G-SRT.6 and G-SRT.8)
i. CB – Exploring Trigonometric Ratios
ii. CC – 4
NCDPI Unpacking:
b) Pearson Geometry Textbook Online Resources
What does this standard mean that a student will
iii. Find the Errors 8.3
know and be able to do?
iv. Activities, Games, and Puzzles 8.3
Students will be able to set up trigonometric ratios in right
c) “Trigonometric Functions” Activity – Omit #3 unless students
triangle problems and use these ratios to find unknown
have already taken Algebra 2.
measures in the triangle.
http://map.mathshell.org/materials/download.php?fileid=846
Bank of G.SRT.7 specific resources:
http://ccssmath.org/?page_id=2285
Sample Assessment Tasks
Skill-based task:
1. A square has a diagonal length of 15 cm.
a. Find the perimeter of the square
b. Find the area of the square
2. Solve for x in the problems below.
Problem Task:
1. “Hopewell Geometry” Activity
o http://map.mathshell.org/materials/download.php?fileid=499
2. David made a ramp for a toy car. The ramp is 3.2 ft long and rises a vertical
distance of 1.5 ft.
a. What is the measure of the angle formed between the ramp and
the ground?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 3
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title:Right Triangle Trigonometry and Pythagorean Theorem
Standard: G-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems
Concepts and Skills to Master:
 Read word problems to construct an accurate/applicable picture
 Use the word problem and the constructed picture to solve the problem.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Order of operations / solving proportions
 Be able to identify the hypotenuse of a right triangle
 Be able to identify which side is opposite of a specific angle
Academic Vocabulary:
Sine, Cosine, Tangent, Opposite side, Adjacent side, Hypotenuse, Angle of Elevation, Angle of Depression, Inverse Function
Suggested Instructional Strategies:
Starting Resources:
This standard should be taught in conjunction with others in this
a) Geometry Textbook Correlation:
cluster (G-SRT.6 and G-SRT.7)
o 8.1 The Pythagorean Theorem and Its
Converse
NCDPI Unpacking:
i. CB – Exploring Trigonometric Ratios
What does this standard mean that a student will know and
o 8.3 Trigonometry
be able to do?
o 8.4 Angle of Elevation & Depression
Students will be able to set up trigonometric ratios in right triangle b) Angle of Elevation & Depression and Law of Sines &
problems and use these ratios to find unknown measures in the
Cosines Review
triangle
o Attached Worksheet
Bank of G.SRT.8 specific resources:
http://ccssmath.org/?page_id=2287
Sample Assessment Tasks
Skill-based task
1. Joanne, who is 5 ft tall, is watching her friend Marjan parasail.
a. If Marjan is 400 ft high, and Joanne is 250 ft away from
the point directly below Marjan, what is the angle of
elevation?
2. In ΔABC, the angle of elevation from C to A is (5m – 37)˚ and
the angle of depression from A to B is (3m – 1)˚.
a. Solve for m
b. Find the measure of Angle A
c. Find the measure of Angle B
d. Find the measure of Angle C
Problem Task
1. 8.4 Enrichment task from www.pearsonsuccessnet.com
2. The task below is a very high level thinking task that also
requires knowledge of circles. Therefore, it should be
completed after covering Unit 8.
http://illustrativemathematics.org/illustrations/607
3. Crystal and Curtis are standing on opposite sides of an 18ft
tree, observing a bird’s nest at the top. If Crystal is 5.5 ft tall
and uses an angle of elevation of 55˚ and Curtis, who is 6 ft
tall, uses an angle of elevation of 43˚, how far apart are
Crystal and Curtis standing?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 4
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title:Right Triangle Trigonometry and Pythagorean Theorem
Standard: G-SRT.9 – Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side
Concepts and Skills to Master:
 Understand the connection/relationship between both formulas for calculating the area of a triangle: A = ½ ab sin(C) and A = ½
bh
 Use the formula A = ½ ab sin(C) to find the area of a non-right triangles when given the measure of two sides and an angle
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Ability to find the area of a triangle. Understand the formula A= ½ bh
 Ability to use basic trigonometry to solve problems
Academic Vocabulary:
Base, height, sine, Opposite side, Hypotenuse
Suggested Instructional Strategies:
Starting Resources:
a) Geometry Textbook Correlation:
 Review area of a triangle first.
a. 10.5 Trigonometry and Area
 Remind students that the height and base used to calculate
b) Pearson Geometry Textbook Online Resources
area must be perpendicular.
a. Activities, Games, and Puzzles 10.5
NCDPI Unpacking:
Bank of G.SRT.9 specific resources:
What does this standard mean that a student will know and
http://ccssmath.org/?page_id=2289
be able to do?
 Students will be able to recognize and explain why A = ½ ab
sin(C) can be used to find the area of non-right triangles
 Students will be able to apply this formula to find the area of
non-right triangles
Sample Assessment Tasks
Skill-based task:

Find the area of the triangle.
Problem Task:
Find the area of the un-shaded region.
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 5
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title:Right Triangle Trigonometry and Pythagorean Theorem
Standard: G-SRT.11 – Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and
non-right triangles (e.g. surveying problems, resultant forces).
Concepts and Skills to Master:
 Use trigonometry to find unknown measures in non-right triangles.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Proportions, order of operations, understanding of basic trigonometry and how to use the inverse function to find angle measures
Academic Vocabulary:Law of Sines, Law of Cosines, Opposite Side, Inverse Function
Suggested Instructional Strategies:
Starting Resources:
 Review proportions and order of operations.
a) Geometry Textbook Correlation:
 Make sure that students use the appropriate case when
o CB: Laws of Sines and Laws of Cosines
labeling their picture (upper-case for angles and lower-case
b) Algebra 2 Textbook Correlation:
for sides). This will prevent confusion when applying the
o 14.4 Area and the Law of Sines
formulas.
o 14.5 Law of Cosines
c) Angle of Elevation & Depression and Law of Sines &
Cosines Review
NCDPI Unpacking:
o Attached Worksheet
What does this standard mean that a student will know and
be able to do?
Bank of G.SRT.11 specific resources:
Students will be able to use trigonometry to find unknown
http://ccssmath.org/?page_id=2293
measures in non-right triangles
Sample Assessment Tasks :
Skill-based task:
1. Solve for x
2. Solve for x
Problem Task:
1. Amapofa County’s airport is shown in
the diagram to the right. A pilot flies
from her home airport at point A to an
airport at point B, and then to an airport
at point C. The pilot wants to know the
distance back to her home airport to
decide if she has enough fuel. How far
is point C from the home airport?
Round your answer to the nearest
tenth.
2. Two wildlife spotters are 2 miles apart on an east-west line.
The spotter in the eastern spot sees a bear 628 north of west
and the other spotter sees the bear 488 north of east. How
far is the bear from each spotter?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 6
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title: Understand congruence in terms of rigid motion.
Standard: G-MG.1 – Use geometric shapes, their measures, and their properties to describe objects (e.g. modeling a tree
trunk or a human torso as a cylinder).
Concepts and Skills to Master:
 Describe everyday objects as geometric shapes and figures.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Ability to identify and classify basic shapes
 Ability to find area and volume of figures
Academic Vocabulary:
Triangle, circle, square, rectangle, trapezoid, cone, cylinder, sphere, hemisphere, prism, pyramid
Suggested Instructional Strategies:
Starting Resources:
a) Geometry Textbook Correlation:
 This standard is not just isolated to this unit. It should
o 10.1, 10.2, 10.3, Areas of Parallelograms, triangles,
reoccur throughout the semester.
trapezoids, rhombuses, kites, and regular polygons
o 10.5 Trigonometry and Area
 Emphasize the relationship between trigonometry, 2D and 3D
o 11.4 and 11.5 Volume of Prisms, Cylinders, Pyramids,
figures, and real-life applications.
and Cones
o
11.6Surface Area and Volume of Spheres
NCDPI Unpacking
o
11.7Areas and Volumes of Similar Solids
What does this standard mean that a student will know and
be able to do?
b) Website
Students will be able to relate and visualize two dimensional and
http://www.shmoop.com/common-core-standards/ccss-hs-g-mgthree dimensional objects as geometric shapes. From these
1.html
connections, students will be able to apply the appropriate
properties to solve problems.
Bank of G.MG.1 specific resources:
http://ccssmath.org/?page_id=2327
Sample Assessment Tasks
Skill-based task:
1. In response to tenant’s requests, the property manager of
your neighborhood has agreed to build a bridge over the
neighborhood pond. If he uses the design below, how long
will the base of the bridge be? (Both sets of stairs are
congruent)
Problem Task:

Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 7
As Blake stands on a diving board, he looks down and spots
a beach ball floating in the cylindrical pool below.
o If the angle of depression from Blake to the beach ball
is 38 degrees, and Blake’s line of sight is 10 feet higher
than the pool, what is the circumference of the pool?
o If the height of the pool is three times larger than the
radius, how many gallons of water will fill the pool?
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title: Interpreting Functions REPEAT TO FOCUS ON TRIG FUNCTIONS
Standard F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms
of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Concepts and Skills to Master:
 Identify the intercepts, relative minimums and maximums, and end behavior of graphs.
 Identify the intervals on which a graph increases and decreases.
 Graph a function based on its key features.
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Graph and identify points on the coordinate plane
 Processes for graphing functions in a calculator
 Locating and identifying parent functions, intercepts, minimum, and maximum values
 Graphing points and evaluating functions
 Ability to read and interpret data from a t-chart
 Understanding the relationship between degree and radian measures
 Simplifying Expressions
Academic Vocabulary:
x-intercept, y-intercept, Minimum value, Maximum value, End Behavior, Interval, Periodicity, Midline
Suggested Instructional Strategies:
Resources:
 Ensure that students can identify intercepts,
a) Algebra 2 Textbook Correlation:
maximum points, minimum points, start and end

13.1 Exploring Periodic Data
behavior, symmetry, and periodicity early in the unit.

13.4 The Sine Function
 Use technology/graph paper to plot key features and

CB 13.4 Graphing Trig Functions
functions.

13.5 Cosine Function

13.6 Tangent Function
 Teach in conjunction with standard F-IF.7 and
A.CED.2

13.7 Translating Sine and Cosine Functions
NCDPI Unpacking:
b) Websites
What does this standard mean that a student will

http://www.purplemath.com/modules/grphtrig.htm
know and be able to do? Students will be able to

http://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_
interpret and understand the graphs of sine and cosine.
5%20GRAPHS%20OF%20SINES%20AND%20COSINES.pdf
They will be able to sketch the graphs given verbal
Bank of F.IF.4 specific resources:
descriptions.
http://ccssmath.org/?page_id=2159
Sample Assessment Tasks
Skill-based task:
Problem Task:(From 2nd website above)
1. For the functionf(t) =
Throughout the day, the depth of water at the end of a dock in Bar Harbor, Maine varies with the tides. The
3sin(2t)…
table shows the depths (in feet) at various times during the morning. (Source: Nautical Software, Inc.)
a. Sketch the graph
 Use a trigonometric function to model the data.
b. Identify the
 Find the depths at 9 A.M. and 3 P.M.
amplitude
 A boat needs at least 10 feet of water to moor at the dock.
c. Identify the period  During what times in the afternoon can it safely dock?
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 8
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORE CONTENT
Cluster Title: Interpreting Functions REPEAT TO FOCUS ON TRIG FUNCTIONS
Standard F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases.
e) Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period,
midline, and amplitude
Concepts and Skills to Master:
• Use equations and graphs to determine key values, intercepts, and maximum and minimum values.
• Use technology to graph functions and determine their key values
SUPPORTS FOR TEACHERS
Critical Background Knowledge:
 Processes for graphing functions in a calculator
 Locating and identifying parent functions, intercepts, minimum, and maximum values
 Graphing points and evaluating functions
 Ability to read and interpret data from a t-chart
 Understanding the relationship between degree and radian measures
 Simplifying Expressions
Academic Vocabulary:
x-intercept, y-intercept, Minimum Value, Maximum Value, Vertex, Radian, Sine, Cosine, End Behavior, Interval, Periodicity, Midline
Suggested Instructional Strategies:
Resources:
a) Algebra 2 Textbook Correlation:
 Review intercepts, minimum, and maximum values of
 13.1 Exploring Periodic Data
functions.
 Demonstrate graphing calculator processes for complex
 13.4 The Sine Function
functions.
 CB 13.4 Graphing Trig Functions
 Teach in conjunction with standard F-IF.4 and A.CED.2
 13.5 Cosine Function
NCDPI Unpacking:
 13.6 Tangent Function
What does this standard mean that a student will know and
 13.7 Translating Sine and Cosine Functions
be able to do? Students will be able to graph the sine and cosine Bank of F.IF.7e specific resources:
functions. They will also be able to identify/calculate the period,
http://ccssmath.org/?page_id=2175
midline, and amplitude for various graphs
Sample Assessment Tasks
Skill-based task:
Problem Task:
Same as F.IF – 4
Same as F.IF – 4
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 9
Course Name:Geometry/Math II
Unit 7
Unit Title: Trigonometry
CORECONTENT
Cluster Title: Algebra
Standard A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales. REPEAT TO FOCUS ON TRIG FUNCTIONS
Concepts and Skills to Master
 Interpret word problems to write and solve right triangle trigonometry problems
SUPPORTS FOR TEACHERS
Critical Background Knowledge
 Basic trigonometry (Soh-Cah-Toa)
 Basic knowledge about right triangles
 Ability to label the sides of a triangle as Hypotenuse, Adjacent, and Opposite
 Ability to solve basic algebra problems
Academic Vocabulary
Sine, Cosine, Tangent, Hypotenuse, Opposite Side, Adjacent Side
Suggested Instructional Strategies
 Teach this throughout the entire unit. Pull this standard into the course
through the use of word problems.
 Limit to graphing sine, cosine, and tangent (right triangle trigonometry).
 Teach with F.IF.4 and F.IF.7
NCDPI Unpacking:
What does this standard mean that a student will know and be able to
do?
Students will be able to interpret word problems into equations with more
than one variable
At this level, extend to simple trigonometric equations that involve right
triangle trigonometry.
(Ex: y = sin (x); y = cos (x); y = tan (x)
Sample Formative Assessment Tasks
Skill-based task
Standards are listed in alphabetical /numerical order not suggested teaching order.
PLC’s must order the standards to form a reasonable unit for instructional purposes.
PAGE 10
Starting Resources:
a) Algebra 2 Textbook Correlation:
 13.4 The Sine Function
 CB 13.4 Graphing Trig Functions
 13.5 Cosine Function
 13.6 Tangent Function
Bank of A.CED.2 specific resources:
http://ccssmath.org/?page_id=2119
Problem Task