Mastering Inverse Trig Functions: Unlocking the Angles

Algebra 2 Grades High School 8:59 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to evaluate inverse trigonometric functions by understanding restricted domains and using the unit circle to find angles. This lesson focuses on sine, cosine, and tangent.

Video Resource

Evaluating Inverse Trig Functions - Find the Angle

Mario's Math Tutoring

Duration: 8:59
Watch on YouTube

Key Concepts

  • Inverse Trigonometric Functions
  • Restricted Domains (Sine, Cosine, Tangent)
  • Unit Circle
  • Radian Measure

Learning Objectives

  • Evaluate inverse sine, cosine, and tangent functions.
  • Determine angles using the unit circle within the restricted domains.
  • Explain why restricted domains are necessary for inverse trig functions to be functions.
  • Convert between degree and radian measures.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic trigonometric functions (sine, cosine, tangent) and their relationship to the unit circle. Introduce the concept of inverse functions and the need for restricted domains.
  • Video Lesson (15 mins)
    Watch the video 'Evaluating Inverse Trig Functions - Find the Angle' by Mario's Math Tutoring. Pay close attention to the examples and explanations of the restricted domains for sine, cosine, and tangent.
  • Unit Circle Review (10 mins)
    Review the unit circle, emphasizing the coordinates of key angles in radians. Practice identifying the sine, cosine, and tangent values for these angles.
  • Guided Practice (15 mins)
    Work through several example problems together, evaluating inverse trigonometric functions. Emphasize the importance of considering the restricted domains. Example problems: sin⁻¹(1/2), cos⁻¹(-√2/2), tan⁻¹(√3).
  • Independent Practice (15 mins)
    Students work independently on a set of problems evaluating inverse trigonometric functions. Provide support and guidance as needed.
  • Wrap-up and Quiz Preview (5 mins)
    Review the key concepts and address any remaining questions. Preview the format of the upcoming quizzes (multiple choice and fill-in-the-blank).

Interactive Exercises

  • Unit Circle Matching Game
    Match angles (in radians) to their corresponding sine, cosine, and tangent values on the unit circle. This can be done using a worksheet or an online interactive tool.
  • Inverse Trig Function Challenge
    A series of problems where students must quickly evaluate inverse trig functions. This can be done as a class competition.

Discussion Questions

  • Why are the domains of trigonometric functions restricted when finding their inverses?
  • How does the unit circle help in evaluating inverse trigonometric functions?
  • Explain the difference in restricted domains for sine, cosine, and tangent.

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Application of Mathematical Concepts

Multiple Choice Questions

Question 1:

What is the range of the inverse sine function, sin⁻¹(x)?

Correct Answer: [-π/2, π/2]

Question 2:

What is the value of cos⁻¹(-1)?

Correct Answer: π

Question 3:

What quadrant is not included in the restricted domain of cosine?

Correct Answer: Quadrant IV

Question 4:

Evaluate tan⁻¹(1).

Correct Answer: π/4

Question 5:

What is the range of the inverse cosine function, cos⁻¹(x)?

Correct Answer: [0, π]

Question 6:

What is the value of sin⁻¹(-1)?

Correct Answer: -π/2

Question 7:

Evaluate cos⁻¹(√3/2).

Correct Answer: π/6

Question 8:

What is the range of the inverse tangent function, tan⁻¹(x)?

Correct Answer: [-π/2, π/2]

Question 9:

What is the value of tan⁻¹(0)?

Correct Answer: 0

Question 10:

The restricted domain for arcsin(x) is?

Correct Answer: [-1, 1]

Fill in the Blank Questions

Question 1:

The inverse of the sine function is written as _______.

Correct Answer: sin⁻¹(x)

Question 2:

The restricted domain of the cosine function ensures that its inverse is a ________.

Correct Answer: function

Question 3:

cos⁻¹(0) is equal to _______.

Correct Answer: π/2

Question 4:

tan⁻¹(√3) is equal to _______.

Correct Answer: π/3

Question 5:

The range of arctangent is between _______ and _______.

Correct Answer: -π/2, π/2

Question 6:

arcsin(1/2) is equal to _______.

Correct Answer: π/6

Question 7:

The restricted domain for arccos(x) is _______.

Correct Answer: [0, π]

Question 8:

sin⁻¹(√2/2) is equal to _______.

Correct Answer: π/4

Question 9:

arccos(-√3/2) is equal to _______.

Correct Answer: 5π/6

Question 10:

arctan(-1) is equal to _______.

Correct Answer: -π/4

Educational Standards

A2.F.1.1:Use algebraic, interval, and set notations to specify the domain and range of various types of functions, and evaluate a function at a given point in its domain. A2.F.1:Understand functions as descriptions of covariation (how related quantities vary together).

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz Export to Google Docs
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans