Algebra 2 (& GT)
Unit 6: Trigonometric Functions
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).
- 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.
- 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.*
- 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.*
- 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.
- 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 two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way 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)
- 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”).
- 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.
- 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.
- 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 two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way 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.
- 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! |