Algebra 2 (& GT)
Unit 7: Trigonometric Functions
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What will my child learn?
Students will:
Extend the domain of trigonometric identities.
F.TF.A.1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle (SAT® Content  ATM.05).
F.TF.A.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.
Analyze functions using different representations.
F.IF.C.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 trigonometric functions, showing period, midline, and amplitude.
Interpret functions that arise in applications in terms of a context.
F.IF.B.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Model periodic phenomena with trigonometric functions.
F.TF.B.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*
Prove and apply trigonometric identities.
F.TF.C.8
Prove the Pythagorean identity sin^2(ø) + cos^2(ø) = 1 and use it to find sin(ø), cos(ø), or tan(ø), given sin(ø), cos(ø), or tan(ø) and the quadrant of the angle.
Students will:
Extend the domain of trigonometric identities.
F.TF.A.1
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle (SAT® Content  ATM.05).
 Background Info.
 Check for Understanding: Radians and Arc Length
 Review/Rewind: Arc Length as a Fraction of Circumference
 Enrichment Tasks: Bicycle Wheel  What Exactly is a Radian?
F.TF.A.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.
 Background Info.
 Check for Understanding: Unit Circle Quiz  Unit Circle Trigonometry Practice
 Review/Rewind: Unit Circle
 Enrichment Tasks: Trig Functions and the Unit Circle  Properties of Trigonometric Functions
Analyze functions using different representations.
F.IF.C.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 trigonometric functions, showing period, midline, and amplitude.
 Check for Understanding: Period of Sinusoidal Functions from a Graph  Graphs of Exponentials and Logarithms  Amplitude of Sinusoidal Functions from a Graph  Midline of Sinusoidal Functions from a Graph
 Review/Rewind: Features of Sinusoidal Functions
 Enrichment Tasks: Exponential Kiss
Interpret functions that arise in applications in terms of a context.
F.IF.B.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
 Background Info.
 Check for Understanding: Interpreting Features of Functions  Positive and Negative Parts of Functions
 Review/Rewind: Interpreting Features of Functions Review
 Enrichment Tasks: As the Wheel Turns  Model Air Plane Acrobatics
Model periodic phenomena with trigonometric functions.
F.TF.B.5
Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*
 Background Info.
 Check for Understanding: Modeling with Periodic Functions  Modeling with Periodic Functions 2
 Review/Rewind: Modeling Daily Temperature  Modeling Annual Temperature  Length of Day
 Enrichment Tasks: Foxes and Rabbits 2  Foxes and Rabbits 3
Prove and apply trigonometric identities.
F.TF.C.8
Prove the Pythagorean identity sin^2(ø) + cos^2(ø) = 1 and use it to find sin(ø), cos(ø), or tan(ø), given sin(ø), cos(ø), or tan(ø) and the quadrant of the angle.
 Background Info.
 Check for Understanding: Circles and Pythagorean Identities  Using the Pythagorean Identity
 Review/Rewind: The Pythagorean Identity
 Enrichment Tasks: Finding Trig Values  Calculations with Sine and Cosine
Additional Standards Assessed on PARCC:
The following standards were taught in previous grades. Check for understanding and review as needed.
Solve system of equations
A.REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (Note: 3x3 system)
Geometry Unit: Applications of Probability
Understand independence and conditional probability and use them to interpret data.
S.CP.A.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”).
S.CP.A.2
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S.CP.A.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
S.CP.A.4
Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities.
S.CP.A.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
The following standards were taught in previous grades. Check for understanding and review as needed.
Solve system of equations
A.REI.C.6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (Note: 3x3 system)
 Background Info.
 Check for Understanding: Graphing Systems of Equations  Systems of Equations
 Review/Rewind: <Insert title/link here>
 Enrichment Tasks: Accurately Weighing Pennies I Estimating a Solution Via Graphs
Geometry Unit: Applications of Probability
Understand independence and conditional probability and use them to interpret data.
S.CP.A.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or”, “and”, “not”).
 Background Info.
 Check for Understanding: Basic Set Notation  Describing Subsets of Sample Spaces
 Review/Rewind: <Insert title/link here>
 Enrichment Tasks: Return to Fred's Fun Factory  Describing Events
S.CP.A.2
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
 Background Info.
 Check for Understanding: Identifying Dependent and Independent Events
 Review/Rewind: <Insert title/link here>
 Enrichment Tasks: Rain and Lightning  Cards and Independence
S.CP.A.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
 Background Info.
 Check for Understanding: Identifying Dependent and Independent Events
 Review/Rewind: <Insert title/link here>
 Enrichment Tasks: Finding Probabilities of Compound Events  Lucky Envelopes
S.CP.A.4
Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities.
 Check for Understanding: Trends in Categorical Data
 Review/Rewind: <Insert title/link here>
 Enrichment Tasks: How Do you Get to School?  Titanic 3
S.CP.A.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
 Background Info.
 Check for Understanding: Trends in Categorical Data
 Review/Rewind: <Insert title/link here>
 Enrichment Tasks: Breakfast Before School  The Titanic 2
What are some signs of student mastery?

Tools & Technology
Desmos is a free online graphing calculator that works on any computer or tablet without requiring any downloads. A FREE Desmos iPad app is available too! Try the Interactive Unit Circle from mathisfun! 