SUBJECT:  PreCal/Trig  

GRADE: 11-12

UNIT TITLE: Unit 6 Trigonometry (cont./Analytic)  

TIME FRAME:

ESSENTIAL QUESTION:  

CCSS Standards

Student-Friendly Objectives

Student Learning Experiences/Tasks

Assessment

Vocabulary

Resources: Literary Works/ Websites/ Chapters

F.TF.4  Use the unit circle to explain symmetry (odd and even) and periodicity of

trigonometric functions

Students will be proficient in the understanding of the basis for odd and even functions in relation to negation and symmetry as well as the repeating nature of these functions.

Students will investigate the unit circle for all 4 quadrants in relation to odd and even functions and application of respective identities in solving problems with and without technology.

Daily bellringers, weekly quizzes, chapter and unit tests, Textbook problems (Ch.5.1), activities, projects

Unit circle, periodicity

Textbook (Ch5.1)

F.TF.5  Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed

Students will master the concept of domain restrictions to determine the inverse function of a give basic function.

Still will perform complete analysis of the various attributes of the six trig functions and state the increasing or decreasing nature of specific intervals and justify.

Textbook problems (Ch5,1)

Increasing, decreasing

Textbook (Ch5.1)

F.TF.7  Use inverse functions

to solve trigonometric equations that arise in modeling contexts; evaluate

the solutions using technology and interpret the

solutions in terms of the context

Students will utilize the graphing calculator to evaluate inverse function properties and comment on the attributes of these functions.

Students will utilize the graphing calculator to assist the interpretation of the behavior of the inverse trig functions for specific intervals.

Textbook problems (Ch5.1,5.2)

Inverse function

Textbook (Ch5.1, 5.2)

F.TF.5  Use trigonometric functions to model physical situations (e.g., harmonic motion, circular motion, area of polygons)

Students will explore various real-world situations that involve simple harmonic motion, circular motion, and the area of poly gons and demonstrate the periodicity of these setting with the use of trigonometric functions.

Students will investigate both text provided physical situations demonstrating periodic motion and real-time animated motion via the Internet for analytical and computational descriptions.

Textbook problems (Ch6.3),Internet problems

Harmonic motion, oscillation, circular motion

Textbook (Ch.5.1, 5,2, 6.3)

Strand  T.4.PC.4  Recognize that some trigonometric equations have infinitely many solutions and be able to state a general formula to represent the infinite solutions

Students will demonstrate their proficiency of understanding that trigonometric functions have a range that is infinite if the domain is not restricted for a particular interval.

Students will investigate and explain function ranges respective of their domains by graphing the function both with and without technology.

Textbook problems (Ch5.1, 5.2, 5.3, 5.4)

Periodic, infinite

Textbook (Ch5.1, 5.4)

G.SRT.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces)

Students will apply both laws proficiently in determining unknown sides and angles of various types of triangles.

Students will explore real-world situations of surveying, navigation, and resultant forces of physics and utilize the Laws of Sines and Cosines to calculate essential measures of distance, direction, and force.

Textbook problems (Ch5.5, 5.6)

Included angle, resultant force,

Textbook (Ch5.5, 5.6