Download Precalculus (Unit 2) - Trigonometric Functions.docx

Wentzville School District
Curriculum Development Template
Stage 1 – Desired Results
Unit 2 - Trigonometric Functions
Unit Title: Trigonometric Functions
Course: Math Analysis
Brief Summary of Unit: In this unit students will use trigonometry to solve triangles. They will use various methods
including right triangle rules, Law of Sines, and Law of Cosines. In addition, students will measure angles using both
degree and radian measure. Students will extend trigonometric properties to angles that are greater than 90 degrees or
less than zero degrees. Students will graph all six trigonometric functions and their inverses. Finally, students will model
and solve real-world problems involving trigonometric functions.
Textbook Correlation: Glencoe PreCalculus Chapter 4
Textbook Correlation: 4 weeks
WSD Overarching Essential Question
Students will consider…
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How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
WSD Overarching Enduring Understandings
Students will understand that…
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Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
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How do I effectively represent quantities and
relationships through mathematical notation?
How accurate do I need to be?
When is estimating the best solution to a
problem?
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Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
strategies.
Concrete understandings in math lead to more
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
recognize periodic phenomena and understand that the situation can be modeled by trigonometric functions.
Meaning
Essential Questions
Understandings
Students will consider…
Students will understand…
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How is trigonometry used to find unknown values?
Why are certain values undefined for certain
functions?
How can you analyze the graphs of sine, cosine,
tangent, cotangent, secant, and cosecant
functions, and their inverses?
When is it best to use radian measure? Degree
measure?
What types of real-world contexts can be modeled
using trigonometric functions?
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The six trigonometric functions and their inverses
can be used to solve problems even when the
relationship does not involve a triangle.
Radians are practical in real world situations.
Relationships in triangles can be used to solve
problems.
Relationships and patterns in the real-world that
are periodic can be modeled using trigonometric
functions.
Acquisition
Acquisition
Key Knowledge
Key Skills
Students will know…
Students will be able to….
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sine
cosine
tangent
cotangent
cosecant
secant
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Convert degree measures to radian measure and
vice versa
Use radians to evaluate arc length, area of a
sector, angular velocity, and linear velocity.
Evaluate trig functions for all angle values
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inverse sine (arcsine, Arcsine)
inverse cosine (arccosine, Arccosine)
inverse tangent (arctangent, Arctangent)
radian measures
reference angle
periodic function
amplitude
frequency
Law of Sines
Law of Cosines
ambiguous case
phase shift
period
coterminal
one to one
arc length
area of a sector
angular velocity
linear velocity
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Find values of trigonometric functions using the
unit circle
Graph all 6 trig functions with changes in
amplitude and period, vertical translation and
phase shift
Model data using sinusoidal functions.
Evaluate inverse trigonometric functions.
Graph inverse trig functions (principal values only)
Solve non-right triangles using the Law of Sines
and Law of Cosines (including the ambiguous case)
Solve real-world problems that involve
trigonometry using multiple strategies.
Standards Alignment
MISSOURI LEARNING STANDARDS
Extend the domain of trigonometric functions using the unit circle.
F-TF-1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
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.
F-TF-3
(+) 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 x, π + x, and 2π - x in terms of their values for x, where x
is any real number.
F-TF-4
(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
F-TF-5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*
F-TF-6
(+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always
decreasing allows its inverse to be constructed.
F-TF-7
(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using
technology, and interpret them in terms of the context.*
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Show Me-Standards
Goal 1: 1, 4, 5, 6, 7, 8
Goal 2: 2, 3, 7
Goal 3: 1, 2, 3, 4, 5, 6, 7, 8
Goal 4: 1, 4, 5, 6
Mathematics: 1, 4, 5