Williamsport Area School District
Mathematics
Grade(s): 11/12
Course Title:
Trigonometry
Unit
Unit Title
Duration
(Days)
1
Angle Measure and
Circular Functions
23
2
Applications of
Trigonometric Functions
28
3
Graphs of Circular
Functions
30
4
Analytic Trigonometry
37
5
Conic Sections
27
6
Explore Exponential and
Logarithmic Functions
19
Tentative
Test Date
Trigonometry
Williamsport Area School District
Unit 1: Angle Measure and Circular Functions
Days: 23
Big Idea:
Angles and their measure.
Unit Essential Question:
How can the measure of an angle be found and what units may
be used to record its size?
Concept
Concept Title
1.1
Angles and their Measure
Duration
(Days)
8
1.2
Radians and Degrees
4
1.3
Relationships between Angle Measurements
and Arc Length
11
Trigonometry
Williamsport Area School District
Concept 1.1
Convert between Degrees and Radians
Lesson Essential
Question(s):
Vocabulary:
How can the measure of an angle be found and what units can by used to
record its size?
standard position, coterminal angles, reference angles, arc length, degreeminute-second, radian, initial side, terminal side, unit circle, positive angle,
negative angle
Descriptor
Eligible
Days
Content
1.1.A Sketching positive angles in standard
3
position (including coterminal and
reference angles)
Learning Goals:
Resources:
1.1.B
Sketching negative angles in standard
position
2
1.1.C
Convert angles to degrees, minutes,
seconds
2
 What is a radian?
http://www.wisc-online.com/objects/ViewObject.aspx?ID=tmh1301


Converting radians to degrees activity with string and wooden circles
TrigTrainer
Assessment Sources:
Notes:
One additional day for re-teaching and/or quiz
Page 3
Trigonometry
Williamsport Area School District
Concept 1.2
Radians and Degrees
Lesson Essential
Question(s):
Additional
Vocabulary:
Learning Goals:
How and why do we convert radians and to degrees and degrees to radians?
Resources:
degrees, radians
Descriptor
Eligible
Content
Days
1.2.A
Convert degrees to radians
1.5
1.2.B
Convert radians to degrees
1.5
TrigTrainers
Assessment Sources:
Notes:
Page 4
Trigonometry
Williamsport Area School District
Concept 1.3
Relationships between Angle Measurements and Arc Length
Lesson Essential
Question(s):
Additional
Vocabulary:
Learning Goals:
Where do we use radian measure and what are their applications?
arc length, sector, linear speed, angular speed
Descriptor
Eligible
Content
Days
1.3.A
Find the arc length of a circle
2
1.3.B
Applications of radian measure
3
1.3.C
Linear Speed and Angular Speed
4
Resources:
Assessment Sources:
Notes:
Experiment- Circular Motion
Page 5
Trigonometry
Williamsport Area School District
Unit 2: Application of Trigonometric Functions
Days: 28
Big Idea: Trigonometric functions can be used to solve triangle applications.
Unit Essential Question:
How can trigonometric definitions be used to solve right and oblique triangle
applications?
Concept
Concept Title
Duration
(Days)
2.1
Trigonometric Functions of Acute Angles
12
2.2
Trigonometric Functions of Non-Acute
Angles
11
2.3
Trigonometric Values
5
Trigonometry
Williamsport Area School District
Concept 2.1
Trigonometric Functions of Acute Angles
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do we find the trigonometric function values of an acute angle in a right
triangle?
sine, cosine, tangent, cotangent, secant, cosecant, co functions
Descriptor
Eligible
Days
Content
2.1.A Unit Circle-and right triangles
2
2.1.B
Right triangle definitions
3
2.1.C
Angle of elevation and angle of
depression
2
2.1.D
Model real-life applications with right
triangles
3
(embedded)
Resources:
Assessment Sources:
Notes:
2.1.A refers to using the TrigTrainer for concrete understanding of sine and
cosine. TrigTrainer uses QI of the unit circle
Page 7
Trigonometry
Williamsport Area School District
Concept 2.2
Trigonometric Functions of Non-Acute Angles
Lesson Essential
Question(s):
Vocabulary:
How can we solve triangles that aren’t right triangles?
Sine, cosine, tangent, cotangent, secant, cosecant, co functions, reference angles, law
of sines, law of cosine, SSA, ASA, SSA, oblique triangles
Learning Goals:
Descriptor
Eligible
Content
Days
2.2.A
Oblique triangles
1
2.2.B
Law of Sines
Solving all cases of triangles (ASA,
SAA, SSA)
3
2.2.C
Law of Cosines
Solving all cases of triangles (SAS, SSS)
2.2.D
Applications of Oblique Triangles
3
3
(embedded)
Resources:
Assessment Sources:
Notes:
Assessment suggested
Page 8
Trigonometry
Williamsport Area School District
Concept 2.3
Trigonometric Values
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do we approximate values of trigonometric functions? How do we find
exact values of trigonometric functions?
Radians, degrees
Descriptor
Eligible
Days
Content
2.3.A Finding function values with a calculator
2
Resources:
2.3.B
Finding angle measures with a calculator
1
2.3.C
Approximate values vs. exact values
1
http://mathmistakes.info/facts/TrigFacts/learn/vals/sum.html
http://www.intmath.com/trigonometric-functions/3-values-trigonometricfunctions.php
Assessment Sources:
Notes:
Page 9
Trigonometry
Williamsport Area School District
Unit 3: Graphs of Circular Functions
Days: 30
Big Idea: What are graphs of circular functions and how can they be applied?
Unit Essential Question:
What are circular functions and how can they be translated?
Concept
Concept Title
Duration
(Days)
9
3.1
Graphs of Sine and Cosine Functions
3.2
Translations of the graphs of Sine and Cosine
Functions
10
3.3
Graphs of Other Circular Functions
11
Page 10
Trigonometry
Williamsport Area School District
Concept 3.1
Graphs of Sine and Cosine Functions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How do we graph sine and cosine?
Where do sine and cosine graphs apply in real life?
Period, amplitude, sinusoidal, domain, range, periodic, cycle
Descriptor
Eligible
Content
3.1.A Graph sine and cosine and establish the
characteristics of the graphs
Days
3
3.1.B
Graph sine and cosine with amplitude and
period changes
3
3.1.C
Write equations of sine and cosine given
their graphs
2
Resources:
Assessment Sources:
Notes:
Page 11
Trigonometry
Williamsport Area School District
Concept 3.2
Translations of the Graphs of Sine and Cosine Functions
Lesson Essential
Question(s):
Hoe do we apply shifts to sine and cosine graphs?
Where do sine and cosine graphs apply in real life?
Vocabulary:
Learning Goals:
Transformations, vertical shift, horizontal/phase shift
Descriptor
Resources:
Eligible
Content
Days
3.2.A
Period, amplitude and vertical shifts
3
3.2.B
Horizontal shifts of sine and cosine
3
3.2.C
Writing equations for sine and cosine
graphs with shifts
3
http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosineamplitude.php
http://www.intmath.com/trigonometric-graphs/2-graphs-sine-cosineperiod.php
http://www.intmath.com/trigonometric-graphs/3-graphs-sin-cos-phaseshift.php
-Oscilloscope
Assessment Sources:
Notes:
Page 12
Trigonometry
Williamsport Area School District
Page 13
Trigonometry
Williamsport Area School District
Concept 3.3
Graphs of the Other Circular Functions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
How can we graph the other circular functions?
Cosecant, secant, tangent, cotangent
Descriptor
Eligible
Content
Days
3.3.A
Graphing tangent and cotangent
4
3.3.B
Matching graphs to equations of cosecant
2
3.3.C
Matching graphs to equations of secant
2
Resources:
Assessment Sources:
Notes:
Page 14
Trigonometry
Williamsport Area School District
Unit 4: Analytic Trigonometry
Days: 37
Big Idea: Fundamental trigonometric identities can be used to evaluate trigonometric functions,
simplify trigonometric expressions and rewrite trigonometric expressions.
Unit Essential Question:
How can trigonometric identities be used to evaluate trigonometric
functions, simplify trigonometric expressions, and rewrite
trigonometric expressions?
Concept
Concept Title
4.1
Using Fundamental Identities
Duration
(Days)
9
4.2
Verifying Trigonometric Identities
10
4.3
Solving Trigonometric Equations
9
4.4
Sum and Difference Formulas
5
4.5
Multiple-Angle Formulas
4
Page 15
Trigonometry
Williamsport Area School District
Concept 4.1
Using Fundamental Identities
Lesson Essential
Question(s):
How are the fundamental trigonometric identities used to evaluate
trigonometric functions?
How are the fundamental trigonometric identities used simplify
trigonometric expressions?
Vocabulary:
Reciprocal identities, quotient identities, Pythagorean Identities, Even/Odd
Identities
Learning Goals:
Resources:
Descriptor
Eligible
Content
Days
4.1.A
Reciprocal Identities
2
4.1.B
Quotient Identities
3
4.1.C
Pythagorean Identities
3
Flip chart with hide/reveal identities filled in.
http://www.bmlc.ca/PureMath30/Pure%20Math%2030%20%20Trigonometry%20Lesson%2011.pdf
Assessment Sources:
Notes:
Page 16
Trigonometry
Williamsport Area School District
Concept 4.2
Verify Trigonometric Identities
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
What strategies are used to verify trigonometric identities?
How do you verify trigonometric identities?
Descriptor
Eligible
Content
Days
4.2.A
Substituting to verify trigonometric
identities
3
4.2.B
Factoring to verify trigonometric
identities
3
4.2.C
3
Using conjugate to verify trigonometric
identities
Resources:
http://www.bmlc.ca/PureMath30/Pure%20Math%2030%20%20Trigonometry%20Lesson%2011.pdf
Assessment Sources:
Notes:
Page 17
Trigonometry
Williamsport Area School District
Concept 4.3
Solving Trigonometric Equations
Lesson Essential
Question(s):
How can algebraic techniques be used to solve trigonometric equations?
How are inverse trigonometric functions used to solve trigonometric
equations?
Trigonometric equations, solutions
Descriptor
Eligible
Days
Content
4.3.A Finding all solutions of a trigonometric
2
equation
4.3.B Using algebra to solve trigonometric
2
equations
Vocabulary:
Learning Goals:
4.3.C
Resources:
Using identities to solve trigonometric
equations
4.3.D Solve trigonometric equations using
inverse functions
6.5 Blitzer Trigonometry 4th Edition
2
2
Assessment Sources:
Notes:
Page 18
Trigonometry
Williamsport Area School District
Concept 4.4
Sum and Difference Formulas (sine and cosine)
Lesson Essential
Question(s):
How are sum formulas used to write and evaluate trigonometric functions?
How are difference formulas used to write and evaluate trigonometric
functions?
Vocabulary:
Learning Goals:
Resources:
Descriptor
Eligible
Content
Days
4.3.A
Use the formula for the cosine of the
difference of two angles.
1
4.3.B
Use sum and difference formulas for
cosines and sines.
3
6.2 Blitzer Trigonometry 4th Edition
Assessment Sources:
Notes:
Page 19
Trigonometry
Williamsport Area School District
Unit 5: Conic Sections
Days: 27
Big Idea: Conic sections have important real life applications, offer good opportunity to extend
analytical thinking, and emphasize the differences between functions and relations.
Unit Essential Question:
How can we recognize conic sections from their equations, what are their
properties and how are they used?
Concept
Concept Title
5.1
Parabolas
Duration
(Days)
7
5.2
Circles and Ellipses
10
5.3
Hyperbolas
10
Page 20
Trigonometry
Williamsport Area School District
Concept 5.1
Parabolas
Lesson Essential
Question(s):
What are the characteristics of a parabola and how can they be used to
determine the graph?
Vocabulary:
Learning Goals:
Parabola, directrix, focus, axis of symmetry
Descriptor
5.1.A
Graph parabolas with vertices at the
origin.
5.1.B
Eligible
Content
Days
1
1.5
Write equations of parabolas in standard
form.
5.1.C
1.5
Graph parabolas with vertices not at the
origin.
5.1.D
Resources:
Solve applied problems involving
parabolas.
10.3 Blitzer Trigonometry 4th Edition
Assessment Sources:
Section Quiz
2
Notes:
Page 21
Trigonometry
Williamsport Area School District
Page 22
Trigonometry
Williamsport Area School District
Concept 5.2
Circles and Ellipses
Lesson Essential
Question(s):
What are the characteristics of a circle and how can they be used to
determine the graph?
What are the characteristics of an ellipse and how can they be used to
determine the graph?
Ellipse, foci, center, vertex (vertices), major axis, minor axis
Descriptor
Eligible
Days
Content
5.2.A Graph circles and ellipses centered at the
3
origin.
Vocabulary:
Learning Goals:
5.2.B
Write equations of circles and ellipses in
standard form.
2
5.2.C
Graph circles and ellipses not centered at
the origin.
2
5.2D
Resources:
Solve applied problems involving
ellipses.
10.1 Blitzer Trigonometry 4th Edition
Assessment Sources:
Section Quiz
2
Notes:
Page 23
Trigonometry
Williamsport Area School District
Concept 5.3
Hyperbolas
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
What are the characteristics of a hyperbola and how can they be used to
determine the graph?
Hyperbola, vertices, foci, branches, transverse axis
Descriptor
Eligible
Days
Content
5.3.A Locate a hyperbola’s vertices and foci to
2
write equations in standard form.
5.3.B
Graph hyperbolas centered at the origin
and not centered at the origin.
5.3.C
Resources:
Solve applied problems involving
hyperbolas.
10.2 Blitzer Trigonometry 4th Edition
Assessment Sources:
Section Quiz
3
3
Notes:
Page 24
Trigonometry
Williamsport Area School District
Unit 6: Explore Exponential and Logarithmic Functions
Days: 19
Big Idea: Exponential and logarithmic functions are related and have many applications to
growth and decay.
Unit Essential Question:
What are the relationships between exponents, radicals, logarithms, exponential
functions and logarithmic functions and how are they useful?
Concept
Concept Title
6.1
Exponential Functions
Duration
(Days)
7
6.2
Logarithmic Functions as Inverses
6
6.3
Logarithms and Logarithmic Functions
6
Page 25
Trigonometry
Williamsport Area School District
Concept 6.1
Exponential Functions
Lesson Essential
Question(s):
Vocabulary:
How can I use exponential functions to model real-life growth and decay?
What is e?
exponent, exponential function, exponential growth, exponential decay,
growth factor, asymptote
Learning Goals:
Descriptor
Eligible
Content
Days
6.1.A
Write equations to graph and model
exponential growth
2
6.1.B
Write equations to graph and model
exponential decay
2
6.1.C
Use functions involving e and their
graphs
2
Resources:
Assessment Sources:
Notes:
Possible project suggested
Page 26
Trigonometry
Williamsport Area School District
Concept 6.2
Logarithmic Functions as Inverses
Lesson Essential
Question(s):
What is the inverse of a function?
How do we find the inverse of an exponential function?
What is a logarithm and how does it relate to exponential functions?
Inverse, logarithm
Descriptor
Eligible
Content
6.2.A Find the inverse of a function graphically
Vocabulary:
Learning Goals:
6.2.B
Find the inverse of an exponential
function
6.2.C
Days
1
1
1
Evaluate basic logarithmic equations
6.2.D
2
Properties of logarithms
Resources:
Assessment Sources:
Notes:
Page 27
Trigonometry
Williamsport Area School District
Concept 6.3
Logarithms and Logarithmic Functions
Lesson Essential
Question(s):
Vocabulary:
Learning Goals:
What are the rules for working with logarithms?
Common logarithm, natural logarithm
Descriptor
Eligible
Content
Days
6.3.A
Evaluate common and natural logarithms
2
6.3.B
Graph logarithmic functions
2
Resources:
Assessment Sources:
Notes:
Page 28