Curriculum  /  Math  /  11th Grade  /  Unit 7: Trigonometric Identities and Equations  /  Lesson 10

Trigonometric Identities and Equations

Lesson 10

Math

Unit 7

11th Grade

Lesson 10 of 16

Objective

Solve trigonometric equations using identities.

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.
  • F.TF.C.8 — Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

Foundational Standards

  • F.TF.A.3
  • F.TF.A.4

Criteria for Success

  1. Solve trigonometric equations using properties of the unit circle and graphs of functions.
  2. Solve trigonometric equations using Pythagorean identities. 

Tips for Teachers

This lesson intentionally avoids excessively complicated algebra or convoluted reasoning. Students should focus on reasoning about the unit circle and applying Pythagorean identities. While there are plenty of more complex ways to apply the idea of solving trig equations, students will be better served by focusing on a deeper dive into a few essential skills.

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Anchor Problems

25-30 minutes

Problem 1

What is the general solution for the equation $${\mathrm{sin}x=\mathrm{csc}x}$$?

Find the solution algebraically and graphically.

Guiding Questions

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Problem 2

What is the general solution for $${\mathrm{sin}^2x+\mathrm{cos}x+1=0}$$?

Guiding Questions

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Target Task

5-10 minutes

What is the general solution for these equations?

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

$${\mathrm{sin}^2x+2\mathrm{cos}x-2=0}$$

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.

  • Include problems that ask students to interpret functions graphically.
  • Include problems involving reciprocal and Pythagorean identities.
  • Include problems that students can visualize using the unit circle, for instance solving $${\mathrm{sin}x=\mathrm{cos}x}$$ by thinking about where sine and cosine are equivalent on the unit circle.
  • Here are some resources to find problems: 

Next

Evaluate expressions using sum and difference formulas.

Lesson 11
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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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