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

Trigonometric Identities and Equations

Lesson 7

Math

Unit 7

11th Grade

Lesson 7 of 16

Objective

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

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

  • Substitute a variable for a more complicated expression to streamline solving equations.
  • Describe how the number of solutions to a trigonometric equation is influenced by the coefficient of $${\theta}$$. 
  • Verify solutions to trigonometric equations graphically. 
  • Determine the solutions to a trigonometric equation over a specified domain.

Tips for Teachers

  • These are two useful YouTube videos on u-substitution with trig. 
  • This lesson uses u-substitution to deal with the solutions to a double and half angle identity problem. This is purposeful—you can bring these problems back later on in the unit. 
  • It will be really valuable for you to have students practice identifying the period of the function, as they will need this to be able to find all of the solutions within a specified domain using $$u$$-substitution.
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Anchor Problems

25-30 minutes

Problem 1

Below are two trigonometric equations and the graphs of the left-hand side of each equation.

$${2\mathrm{cos}x+1=3}$$ $${2\mathrm{cos}\left({x\over2}\right)+1=3}$$

How are the equations and the graphs similar? Different?

Guiding Questions

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Problem 2

Find all of the solutions, algebraically, within the domain $${0\leq x \leq 2\pi}$$.

$${2\mathrm{sin}(2x)+2=3}$$

Guiding Questions

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Problem 3

Solve:

$${-3\mathrm{tan}\left({\pi\over2}x\right)=\sqrt3}$$

Guiding Questions

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Target Task

5-10 minutes

Write a general solution for:

a.   $${2\mathrm{cos}(2x)-\sqrt3=0}$$

b.  $${-\mathrm{tan}(3x)=1}$$

Next

Use inverse trigonometric functions to solve contextual problems.

Lesson 8
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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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