Curriculum  /  Math  /  11th Grade  /  Unit 7: Trigonometric Identities and Equations  /  Lesson 14

Trigonometric Identities and Equations

Lesson 14

Math

Unit 7

11th Grade

Lesson 14 of 16

Objective

Use trigonometric identities to analyze graphs of functions.

Common Core Standards

Core Standards

  • 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.
  • 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. Reason about the solutions to trigonometric equations without solving for exact solutions.
  2. Rewrite equations to analyze graphs of functions.
  3. Identify intersection points of graphs from functions.
  4. Reason about domain restrictions to find intersection points of graphs. 

Tips for Teachers

This lesson synthesizes skills from the unit as a whole. While many students will have already mastered these skills, this provides an opportunity to explore more deeply as well as space to review skills and target problems toward what students have struggled with.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

Given that

$${f(x)={{\mathrm{cos}x+\mathrm{sin}x}\over\mathrm{cos}(2x)}}$$

$${g(x)={1\over{\mathrm{cos}x\mathrm{sin}x}}}$$

Answer the following questions:

  1. Identify where both functions are undefines over the domain of $${0 \leq x \leq 2\pi}$$.
  2. Show that, where defined, $${f(x)= g(x)}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Fill in the blanks below using a number from $$1$$ to $$9$$ (no repeating), to find the equation whose solution is the largest value of $$x$$ (from $$0$$ to $$360$$, or $$0$$ to $${2\pi}$$). What numbers will give you the smallest value of $$x$$?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Open Middle Solving Trigonometric Equations

Solving Trigonometric Equations by is made available on Open Middle under the CC BY-NC-SA 4.0 license. Accessed May 21, 2018, 2:59 p.m..

Target Task

5-10 minutes

Given:

$${{f(x)}=\mathrm{cos}(2x)}$$

$${g(x)=-\mathrm{cos}(x)}$$

a.   Describe the period, amplitude, and midline of the function $${f(x)}$$.

b.   Where is $${f(x)}=g(x)$$ over the domain of $${0\leq x \leq 2\pi}$$?

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 finding where two functions are equivalent.
  • Include graphing problems that require rewriting using identities.
  • Include problems asking students to compare values reasoning with the unit circle without actually evaluating, like Anchor Problem #2.
  • Include problems reviewing skills that students have struggled with in the unit as a whole.

Next

Use the Law of Sines to find missing side lengths and angle measures in acute triangles.

Lesson 15
icon/arrow/right/large

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

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free