Trigonometric Functions

10 Components
Initial Task
Remote Measures
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4
Formative Assessment Lesson
Ferris Wheel
Re-engagement
Re-engagement for Unit 3
End of Unit Assessments
End of Unit Assessment for Unit 3 End of Unit Assessment Teacher Resources ALG II Unit 3 Find aligned Regents questions with Quiz Banker
A2 U3: Trigonometric Functions
Unit Outline
Initial Task
Remote Measures
Big Ideas
Big Idea 1 Big Idea 2 Big Idea 3 Big Idea 4
Formative Assessment Lesson
Ferris Wheel
Re-engagement
Re-engagement for Unit 3
End of Unit Assessments
End of Unit Assessment for Unit 3 End of Unit Assessment Teacher Resources ALG II Unit 3 Find aligned Regents questions with Quiz Banker
None
A2 U3:

Trigonometric Functions

How can we model periodic behavior?
5 weeks
See Standards
Common Core: Major Standards:
F-IF.B.4

Interpret functions that arise in applications in terms of the context. 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.

Common Core: Supporting Standards:
F-IF.C.7e

Analyze functions using different representations. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Common Core: Additional Standards:
F-TF.A.1

Extend the domain of trigonometric functions using the unit circle. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.A.2

Extend the domain of trigonometric functions using the unit circle. 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.B.5

Model periodic phenomena with trigonometric functions. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

F-TF.C.8

Prove and apply trigonometric identities.  Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

The core mathematics of this unit is about understanding cyclical relationships between two quantities. Students develop a conceptual understanding of the repetition belonging to periodic functions and using this foundation for interpreting features of trigonometric functions including period, frequency, and amplitude. This unit builds on student experiences from geometry with trigonometric ratios, radian measure, and triangle applications to understand the unit circle as a tool for creating and analyzing trigonometric functions.

Essential Questions:

  • What makes a function periodic?
  • How are sine and cosine examples of a periodic function?
  • How can we model periodic behavior?
  • How do we compare different ways of measurement?
Printable Unit Plan

Unit Outline

10 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 4 itemsHide 4 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 1 itemHide 1 item

End of Unit Assessments See 3 itemsHide 3 items