Trigonometric Identities and Equations

Lesson 8

Math

Unit 7

11th Grade

Lesson 8 of 16

Objective


Use inverse trigonometric functions to solve contextual problems.

Common Core Standards


Core Standards

  • F.TF.B.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.

Foundational Standards

  • F.BF.B.3

Criteria for Success


  1. Identify the features of a function in a graphical or algebraic model and relate them to the context they represent. 
  2. Write equations in sine and cosine to model periodic functions. 
  3. Use inverse trigonometric functions to find solutions to contextual problems.
  4. Verify solutions graphically. 

Tips for Teachers


Many of the problems presented are climate related, but it is important for students to see other kinds of functions besides these. 

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

The average monthly temperature, in degrees Celsius, in a coastal city in the United States is periodic and can be modeled with the equation $${y=-8\mathrm{cos}\left((x-1)\left(\pi\over6\right)\right)+17.5}$$, where $$x$$ represents the month, $$x=1$$ represents January, and $$y$$ represents the average temperature in degrees Celsius. 

Below is the graph of the equation. 

A tourist wants to visit the city when the average temperature is closest to 25℃. What recommendations would you make regarding when the tourist should travel?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 14Exercise 2

Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Do the activity Burning Daylight by Desmos. Skip slides 6 and 7.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Desmos Burning Daylight

Burning Daylight by Desmos is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed May 21, 2018, 2:21 p.m..

Target Task


The estimated size for a population of rabbits and a population of coyotes in a desert habitat are shown in the table. The estimated population sizes were recorded as a part of a long-term study related to the effect of commercial development on native animal species.

Years since initial count (n) 0 3 6 9 12 15 18 21 24
Estimated number of rabbits (r) 14,989 10,055 5,002 10,033 15,002 10,204 4,999 10,002 14,985
Estimated number of coyotes (c) 1,995 2,201 2,003 1,795 1,999 2,208 2,010 1,804 2,001

Below are sketches of each graph, with a curve fitted to the data.

Write the function for each situation and then calculate the two different numbers of years where the population estimate is about 13,000 for rabbits and 2,100 for coyotes.

References

EngageNY Mathematics Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 14Exercise 3

Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

icon/arrow/right/large copy

Lesson 7

icon/arrow/right/large

Lesson 9

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Basic Trigonometric Identities and Equivalent Expressions

Topic B: Solve Trigonometric Equations

Topic C: Advanced Identities and Solving Trigonometric Equations

Topic D: Applications and Extensions of Trigonometric Functions

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free