Trigonometric Identities and Equations

Lesson 4

Math

Unit 7

11th Grade

Lesson 4 of 16

Objective


Find angle measures using inverse trig functions in right triangles.

Common Core Standards


Core Standards

  • F.TF.B.6 — Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  • 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

  • G.SRT.C.6

Criteria for Success


  1. Identify and use notation for inverse trig functions ($${\mathrm{arcsin/sin}^{-1}}$$, $${\mathrm{arccos/cos^{-1}}}$$). 
  2. Use the inverse notation to solve for missing angles in right triangles. 
  3. Use a calculator in degree and radian mode to find missing angles represented in degrees and radians. 
  4. Describe the domain of the inverse functions when solving angle measures in right triangles.
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Anchor Problems

25-30 minutes


Problem 1

Below are sets of three equations that are equivalent. Find $$x$$ for each set of equations.

$$\mathrm{sin}x=1$$ $$\mathrm{arcsin}1=x$$ $$\mathrm{sin}^{-1}1=x$$
$${\mathrm{cos}x}={{\sqrt3}\over2}$$ $$\mathrm{arccos}{{\sqrt3}\over2}=x$$ $$\mathrm{cos}^{-1}{\sqrt3\over2}=x$$

Guiding Questions

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Problem 2

Solve the following equations. Write your answers in radians.

$${\mathrm{sin}x={1\over2}}$$

$${\mathrm{cos}^{-1}\left({\sqrt2\over2}\right)=x}$$

$${\mathrm{arcsin}(0.35)=x}$$

Guiding Questions

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Target Task

5-10 minutes


Find two values where $${\mathrm{cos}x=-1}$$.

What is $${\mathrm{arccos}(-1)}$$?

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 solving right triangles using inverse trigonometric functions. 
  • Include problems where a calculator is necessary.
  • Include error analysis problems where the calculator is in radian mode, not degree mode, and vice versa.

Next

Analyze inverse trigonometric functions graphically.

Lesson 5
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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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