Trigonometric Identities and Equations

Lesson 5

Math

Unit 7

11th Grade

Lesson 5 of 16

Objective


Analyze inverse trigonometric functions graphically.

Common Core Standards


Core Standards

  • F.BF.B.4.D — Produce an invertible function from a non-invertible function by restricting the domain.
  • F.IF.C.7.E — Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • 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.8

Criteria for Success


  1. Describe domain restrictions on inverse trigonometric functions. 
  2. Describe why there could be infinite solutions to a system of a linear function and a periodic function. 
  3. Identify solutions to simple trigonometric equations graphically and algebraically.
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Anchor Problems


Problem 1

Below is a student's answer (in three steps, left to right) to the following problem:

Graph the inverse of the function $${y=\mathrm{sin}x}$$.

What did the student do in each step?

What did the student do well?

How can the student's answer be improved?

Guiding Questions

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Problem 2

What is the solution to the system of:

$$\left\{\begin{matrix} y=\mathrm{cos}x\\ y=-1 \end{matrix}\right.$$

Guiding Questions

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Target Task


Find points of intersection of the following functions:

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

$${g(x)={-\sqrt3\over 2}}$$

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 practice evaluating inverse trig functions for values on the unit circle.
  • Include problems requiring a calculator.
  • Include problems with and without domain restrictions.
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Lesson 4

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Lesson 6

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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