Curriculum  /  Math  /  11th Grade  /  Unit 7: Trigonometric Identities and Equations  /  Lesson 12

Trigonometric Identities and Equations

Lesson 12

Math

Unit 7

11th Grade

Lesson 12 of 16

Objective

Solve equations and prove identities using sum and difference formulas.

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

Criteria for Success

  1. Use the sum and difference formulas to verify cofunction identities. 
  2. Use sum and difference formulas to rewrite equations.
  3. Solve trigonometric equations using sum and difference formulas.
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Anchor Problems

25-30 minutes

Problem 1

Prove the cofunction identity of:

$${\mathrm{cos}\left({\pi\over2}-x\right)=\mathrm{sin}x}$$

Using the sum or difference formula.

Guiding Questions

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Problem 2

Solve:

$${\mathrm{sin}\left(x+{\pi\over4}\right)+1=\mathrm{sin}\left({\pi\over4}-x\right)}$$ for $${0 \leq x \leq 2\pi}$$.

Guiding Questions

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Target Task

5-10 minutes

Find the general solution for:

$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$

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.

  • Prove other cofunction identities using the sum and difference formulas.
  • Prove periodic identities using the sum and difference formulas.
  • Include error analysis problems. 
  • Ensure that students check solutions with a calculator. 

Next

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

Lesson 13
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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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