Curriculum  /  Math  /  11th Grade  /  Unit 7: Trigonometric Identities and Equations  /  Lesson 13

Trigonometric Identities and Equations

Lesson 13

Math

Unit 7

11th Grade

Lesson 13 of 16

Objective

Derive double angle formulas and use them to solve equations and prove identities.

Common Core Standards

Core Standards

  • F.TF.C.9 — Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Foundational Standards

  • F.TF.A.3
  • F.TF.A.4

Criteria for Success

  1. Derive the double angle formulas from the sum formulas.
  2. Explain that doubling an angle does not double the value of the sine, cosine, or tangent.
  3. Prove identities using double angle formulas.
  4. Solve equations using double angle formulas.

Tips for Teachers

The Georgia Standards of Excellence Curriculum Frameworks by the Georgia Department of Education that is referenced in Anchor Problem #1 and the Problem Set Guidance for this lesson is great for a lot of explanations, including the tangent guiding questions of Anchor Problem #1.

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Anchor Problems

25-30 minutes

Problem 1

Use the sum formula to determine a formula for finding the sine, cosine, and tangent of a double angle.

$${\mathrm{sin}(a+a)=}$$

$${\mathrm{cos}(a+a)=}$$

$${\mathrm{tan}(a+a)=}$$

Guiding Questions

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Problem 2

Is the following statement true or false? 

“If an angle is doubled, then the sine value of the angle is doubled.”

  • Write an equation that describes the statement. 
  • Explain your reasoning algebraically.
  • Explain your reasoning using the graph shown.

Guiding Questions

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References

Problem 3

Prove the following identity:

$${{{\mathrm{cos}2x}\over{\mathrm{sin}x+\mathrm{cos}x}}=\mathrm{cos}x-\mathrm{sin}x}$$

Guiding Questions

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Target Task

5-10 minutes

Solve the equation for $${0 \leq x \leq 2\pi}$$.

$${\mathrm{sin}2x\mathrm{cos}x=\mathrm{sin}x}$$

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.

Next

Use trigonometric identities to analyze graphs of functions.

Lesson 14
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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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