# Unit of Study Trigonometric Functions (Chapter 4)

Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community.

Course Number 440/441 Title TRIG/PRECAL (A & B) HONORS Grade 11-12 # of Days 120
Course Description / This intensive course completes the ideas of precalculus mathematics.
Part A topics include trigonometricfunctions, circular functions, trigonometric applications, trigonometric functions and proofs.
Part B topicsinclude analyzing all types of algebraic functions, exponential functions, conic sections and an introduction tocalculus.
Student owned graphing calculators are necessary for class work and homework in this course.This course is designed for those students who have shown an exceptional interest and ability in GeometryHonors and Algebra II Honors. Students planning to take AP Calculus should take this course.
Instructional Strategies / Instructional Strategies include but may not be limited to the following:
• Direct instruction
• Group work
• Individual student work
• Projects
• Quizzes
• Tests
• Games

Student Learning Expectations / 1.Read, write and communicate effectively.
2.Utilize technologies appropriately and effectively.
3.Apply critical thinking skills.
4.Explore and express ideas creatively.
5.Participate in learning both individually and collaboratively.
6.Demonstrate personal, social, and civic responsibility.

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Unit of Study Trigonometric Functions (Chapter 4)

MA Standard/Strands: / Trigonometric Functions F.TF
Extend the domain of trigonometric functions using the unit circle.
1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
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.
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 π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
4. (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Model periodic phenomena with trigonometric functions.
5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
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.
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. 
Prove and apply trigonometric identities.
8. Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant.
9. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Time Frame: / 35 days (the breakdown of the days include review and quiz days as well as instruction days)
Text
(Chapter/Pages) / Text: PRECALCULUS Essentials 3e, Robert Blitzer, Pearson, 2010
Chapter 4, pages 459 - 566
Other Resources: / Precalculus: Graphical, Numerical, Algebraic, Demana, 2001
Essential Questions
Concepts, Content: / 4.1 Angles and Radian Measure (7 days)
• Recognize and use the vocabulary of angles
• Use degree and radian measure
• Convert between degrees and radians
• Sketch angles in standard position and find coterminal angles
• Find the length of a circular arc
• Use linear and angular speed to describe motion on a circular path
11 days (4.1 – 4.4)
4.2 Trigonometric Functions: The Unit Circle
• Use a unit circle to define trigonometric functions of real numbers
4.3 Right Triangle Trigonometry
• Use right triangles to evaluate trigonometric functions
• Find exact values of trig functions for 30o, 60o and 45o
• Use equal cofunctions of complements
• Use right triangle trigonometry to solve applied problems
4.4 Trigonometric Functions of Any Angle
• Use the definitions of trigonometric functions of any angle
• Use the SIGNS of the trigonometric functions
• Find reference angles
• Use reference angles to evaluate trigonometric functions
4.5 Graphs of Sine and Cosine Functions (7 days)
• Understand the graph of y = sin x and y = cos x
• Graph transformations of y = sin x and y = cos x, by graphing y = A sin B(x – C) + D and
y = A cos B(x –C) + D
4.6 Graphs of Other Trigonometric Functions (2 days)
• Understand and graph variations of y = tan x, y = cot x, y = sec x and y = csc x
1.8 Inverse Functions , p. 232 – 243 (2 days)
• Review characteristics of Inverse Functions
• Vertical Line Test
• Horizontal Line Test
• One-to-One Functions
4.7 Inverse Trigonometric Functions (3 days)
• Understand and use the inverse sine, cosine and tangent functions
• Use a calculator to evaluate the inverse trigonometric functions
• Find the exact values of composite functions with inverse trigonometric functions
4.8 Applications (3 days)
• Solve a right triangle
• Solve problems involving bearings
• Model simple harmonic motion

Targeted Skill(s): /
• Use degree and radian measure
• Convert between degrees and radians
• Sketch angles in standard position and find coterminal angles
• Find the length of a circular arc
• Use linear and angular speed to describe motion on a circular path
• Use right triangles to evaluate trigonometric functions
• Find exact values of trig functions for 30o, 60o and 45o
• Use the definitions of trigonometric functions of any angle
• Use the SIGNS of the trigonometric functions
• Use reference angles to evaluate trigonometric functions
• Understand the graph of y = sin x and y = cos x
• Graph transformations of y = sin x and y = cos x, by graphing y = A sin B(x – C) + D and
y = A cos B(x –C) + D
• Understand and graph variations of y = tan x, y = cot x, y = sec x and y = csc x
• Understand and use the inverse sine, cosine and tangent functions
• Use a calculator to evaluate the inverse trigonometric functions
• Find the exact values of composite functions with inverse trigonometric functions
• Solve a right triangle
• Solve problems involving bearings
• Model simple harmonic motion

Writing: / Writing components are integrated throughout the homework assignments
Assessment Practices: / QUIZZES
• Quiz 4.1
• Quiz 4.2 – 4.4
• Quiz 4.5
• Quiz 4.6
• Quiz 1.8 & 4.7 – 4.8
PROJECTS
• Mnemonic Device Project to memorize trig ratios
• Ferris Wheel Project: Construct a working Ferris wheel. Write an equation to model a person’s height off the ground as the ride the Ferris wheel. Sketch one period of the person’s ride.
GAMES
• Starship: A Battleship style game using a polar graph and using radian measures to name the locations
• Board Game with Trig Function Dice: Designed to practice exact values

Unit of Study Analytic Trigonometry (Chapter 5)

MA Standard/Strands: / Trigonometric Functions F.TF
Prove and apply trigonometric identities.
8. Prove the Pythagorean identity sin2 (θ) + cos2(θ) = 1 and use it find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant.
9. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Time Frame: / 20 days
(The remaining 5 days of the trimester will be used to review for and take a trimester exam)
Text
(Chapter/Pages) / Text: PRECALCULUS Essentials 3e, Robert Blitzer, Pearson, 2010
Chapter 5, pages 585 - 642
Other Resources: / Precalculus: Graphical, Numerical, Algebraic, Demana, 2001
Essential Questions
Concepts, Content: / 5.1 Verifying Trigonometric Identities (4 days)
• Establish the fundamental trigonometric identities
• Use the fundamental trigonometric identities to verify identities (proofs)
5.2 Sum and Difference Formulas (Identities) (5 days)
• Apply the identities to actual problems with angles
• Apply the identities to verify identities
5.3 Double-Angle, Power-Reducing and Half-Angle Formulas (Identities) (4 days)
• Apply the identities to actual problems with angles
• Apply the identities to verify identities
5.5 Trigonometric Equations (5 days)
• Find all solutions of a trigonometric equation
• Solve equations with multiple angles
• Solve trigonometric equations in quadratic form
• Using factoring to separate different functions in trigonometric equations
• Use identities to solve trigonometric equations

Targeted Skill(s): /
• Establish the fundamental trigonometric identities
• Use the fundamental trigonometric identities to verify identities (proofs)
• Apply the Sum and Difference, Double-Angle, Power-Reducing and Half-Angle identities to actual problems with angles
• Apply the Sum and Difference, Double-Angle, Power-Reducing and Half-Angle identities to verify identities
• Find all solutions of a trigonometric equation
• Solve equations with multiple angles
• Solve trigonometric equations in quadratic form
• Using factoring to separate different functions in trigonometric equations
• Use identities to solve trigonometric equations

Writing: / Writing components are integrated throughout the homework assignments
Assessment Practices: / QUIZZES
• Quiz 5.1
• Quiz 5.2
• Quiz 5.3
• Quiz 5.5
PROJECTS
• Polar Graphing Project: students investigate the families of polar graphs with their graphing calculators

Unit of Study

MA Standard/Strands:
Time Frame:
Text
(Chapter/Pages)
Other Resources:
Essential Questions
Concepts, Content:
Targeted Skill(s):
Writing:
Assessment Practices:

Unit of Study

MA Standard/Strands:
Time Frame:
Text
(Chapter/Pages)
Other Resources:
Essential Questions
Concepts, Content:
Targeted Skill(s):
Writing:
Assessment Practices:

Unit of Study

MA Standard/Strands:
Time Frame:
Text
(Chapter/Pages)
Other Resources:
Essential Questions
Concepts, Content:
Targeted Skill(s):
Writing:
Assessment Practices:

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