Curriculum  /  Math  /  11th Grade  /  Unit 7: Trigonometric Identities and Equations  /  Lesson 6

Trigonometric Identities and Equations

Lesson 6

Math

Unit 7

11th Grade

Lesson 6 of 16

Objective

Solve linear trigonometric equations.

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.TF.A.3
  • F.TF.A.4

Criteria for Success

  1. Describe how solving a linear trigonometric equation is like solving a linear equation. 
  2. Describe how solving trig equations is similar to finding the solution(s) to a system of equations, graphically and algebraically.
  3. Describe the number of solutions in trigonometric equations within a specified domain. Explain the difference between solutions with a function and its inverse with restricted domain. 
  4. Identify, based on the sign of the solution, the number and value of the solutions within the specified domain of the equation using the unit circle.

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Anchor Problems

25-30 minutes

Problem 1

We did these problems a few lessons ago when we were solving for angles in right triangles. 

$${\mathrm{sin}x={1\over2}}$$

$${\mathrm{cos}^{-1}\left(\sqrt2\over2\right)=x}$$

Which has infinite solutions and which has only one solution? Describe your reasoning.

Guiding Questions

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Problem 2

Find all the solutions within the domain of $${0 \leq x \leq 2\pi}$$ for the following equation.

$${2\mathrm{cos}(x)-1=0}$$

Guiding Questions

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Target Task

5-10 minutes

Problem 1

Solve each trigonometric equation such that $${0\leq x\leq2\pi}$$. Give answers in exact form.

$${2\mathrm{sin}(x)+\sqrt3=0}$$

References

EngageNY Mathematics Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 12 — Exit Ticket, Question #2a

Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 12 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..

Problem 2

Solve the trigonometric equation such that $${0\leq x\leq2\pi}$$. Round to three decimal places.

$${\sqrt5\mathrm{cos}(x)-2=0}$$

References

EngageNY Mathematics Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 12 — Exit Ticket, Question #3

Precalculus and Advanced Topics > Module 4 > Topic C > Lesson 12 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..

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.

  • Explain what the solution$${{\pi\over3}+2\pi k}$$ means. Can you determine the domain that this solution is under? Why or why not? 
  • Include problems that ask students to solve within a specified domain and to find all real solutions.
  • Include problems that can be solved with the unit circle and problems requiring a calculator.

Next

Solve linear trigonometric equations using $$u$$-substitution.

Lesson 7
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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

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