Unlocking Coterminal Angles: A Comprehensive Guide

Algebra 2 Grades High School 9:15 Video
Print Lesson Plan Watch Video

Lesson Description

Explore coterminal angles in degrees and radians, understand how to find them, and practice with examples.

Video Resource

Coterminal Angles

Kevinmathscience

Duration: 9:15
Watch on YouTube

Key Concepts

  • Coterminal angles
  • Degrees and radians
  • Terminal side

Learning Objectives

  • Define coterminal angles and explain their relationship to the terminal side.
  • Calculate coterminal angles in degrees by adding or subtracting multiples of 360 degrees.
  • Calculate coterminal angles in radians by adding or subtracting multiples of 2π.

Educator Instructions

  • Introduction to Coterminal Angles (5 mins)
    Begin by defining angles, their measurement in degrees and radians, and the concept of a terminal side. Introduce the term 'coterminal angles' and explain that these are angles that share the same terminal side.
  • Coterminal Angles in Degrees (10 mins)
    Explain how to find coterminal angles in degrees by adding or subtracting multiples of 360°. Provide examples and work through them step-by-step. Emphasize that adding or subtracting 360° results in landing on the same terminal side.
  • Coterminal Angles in Radians (15 mins)
    Explain how to find coterminal angles in radians by adding or subtracting multiples of 2π. Discuss finding common denominators when adding or subtracting fractions involving π. Provide examples and work through them step-by-step.
  • Practice Problems and Examples (15 mins)
    Work through a variety of examples, including finding both positive and negative coterminal angles in both degrees and radians. Encourage student participation and questions. Show how to find multiple coterminal angles by repeatedly adding or subtracting 360° or 2π.
  • Wrap-up and Review (5 mins)
    Summarize the key concepts of coterminal angles, degrees, and radians. Reiterate the methods for finding coterminal angles. Preview upcoming topics related to trigonometry.

Interactive Exercises

  • Angle Generator
    Use an online tool or create a worksheet where students are given an angle in degrees or radians and must find a positive and a negative coterminal angle.
  • Terminal Side Matching
    Provide a set of angles and a set of terminal side diagrams. Students must match each angle with its corresponding terminal side, identifying coterminal angles along the way.

Discussion Questions

  • Why do coterminal angles share the same trigonometric values?
  • How can you determine if two angles are coterminal without graphing them?
  • Are there an infinite number of coterminal angles for any given angle? Why or why not?

Skills Developed

  • Angle manipulation
  • Fraction arithmetic
  • Conceptual understanding of angles

Multiple Choice Questions

Question 1:

Which of the following angles is coterminal with 60°?

Correct Answer: 420°

Question 2:

Which of the following angles is NOT coterminal with 150°?

Correct Answer: 610°

Question 3:

What is a positive coterminal angle of -45°?

Correct Answer: 315°

Question 4:

Which angle is coterminal with π/2 radians?

Correct Answer: 5π/2

Question 5:

Which of the following is a negative coterminal angle for 3π/4 radians?

Correct Answer: -5π/4

Question 6:

If an angle is 7π/6 radians, a coterminal angle could be:

Correct Answer: 19π/6

Question 7:

Two angles are coterminal if they share the same:

Correct Answer: Terminal side

Question 8:

Adding or subtracting what value results in a coterminal angle in degrees?

Correct Answer: 360°

Question 9:

Adding or subtracting what value results in a coterminal angle in radians?

Correct Answer: 2π

Question 10:

What is a coterminal angle of 0 degrees?

Correct Answer: 360°

Fill in the Blank Questions

Question 1:

Angles that share the same ___________ side are called coterminal angles.

Correct Answer: terminal

Question 2:

To find a coterminal angle in degrees, you can add or subtract multiples of ___________ degrees.

Correct Answer: 360

Question 3:

To find a coterminal angle in radians, you can add or subtract multiples of ___________.

Correct Answer: 2π

Question 4:

A positive coterminal angle for -100° is ___________.

Correct Answer: 260°

Question 5:

A negative coterminal angle for 50° is ___________.

Correct Answer: -310°

Question 6:

A positive coterminal angle for -π/3 radians is ___________.

Correct Answer: 5π/3

Question 7:

A negative coterminal angle for π/4 radians is ___________.

Correct Answer: -7π/4

Question 8:

Adding 720° to an angle will result in a ___________ angle.

Correct Answer: coterminal

Question 9:

Subtracting 4π from an angle will result in a ___________ angle.

Correct Answer: coterminal

Question 10:

The angle 450 degrees is coterminal to _______ degrees.

Correct Answer: 90

Educational Standards

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