Unlocking Coterminal Angles: Navigating the Unit Circle

PreAlgebra Grades High School 1:42 Video
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Lesson Description

Explore coterminal angles, learn how to find them in both degrees and radians, and understand their significance on the unit circle. This lesson provides a clear understanding of coterminal angles and their applications.

Video Resource

Coterminal Angles

Mario's Math Tutoring

Duration: 1:42
Watch on YouTube

Key Concepts

  • Coterminal Angles
  • Radian Measure
  • Degree Measure
  • Unit Circle

Learning Objectives

  • Define coterminal angles and explain their relationship to the unit circle.
  • Calculate coterminal angles in both degrees and radians by adding or subtracting multiples of 360 degrees or 2π radians.
  • Identify and determine both positive and negative coterminal angles for a given angle.

Educator Instructions

  • Introduction (5 mins)
    Begin by defining coterminal angles and explaining the meaning of 'co-' and 'terminal'. Briefly review the unit circle and its significance in trigonometry. Introduce the concept that coterminal angles share the same terminal side.
  • Finding Coterminal Angles (10 mins)
    Explain the method for finding coterminal angles: adding or subtracting 360 degrees (or 2π radians) to a given angle. Emphasize that multiple additions or subtractions can be performed to find different coterminal angles. Show examples of finding coterminal angles for both degree and radian measures.
  • Examples and Practice (10 mins)
    Work through examples of finding one positive and one negative coterminal angle for various given angles. Include examples that require multiple additions or subtractions of 360 degrees (or 2π radians) to obtain a negative angle. Provide students with practice problems to solve independently.
  • Real-World Applications and Wrap-up (5 mins)
    Briefly discuss real-world applications of coterminal angles, such as in navigation or periodic phenomena. Summarize the key concepts and reiterate the method for finding coterminal angles. Answer any student questions.

Interactive Exercises

  • Coterminal Angle Challenge
    Present students with a series of angles and have them find both a positive and a negative coterminal angle for each. Increase the difficulty by using larger angle measures or radian values requiring multiple additions/subtractions.
  • Unit Circle Matching
    Create a matching game where students match angles with their coterminal angles on a unit circle diagram.

Discussion Questions

  • Why do coterminal angles have the same trigonometric values?
  • Can an angle have an infinite number of coterminal angles? Explain.
  • How does understanding coterminal angles help in simplifying trigonometric problems?

Skills Developed

  • Angle manipulation
  • Radian and degree conversion
  • Unit circle understanding
  • Problem-solving

Multiple Choice Questions

Question 1:

Which of the following angles is coterminal with 45°?

Correct Answer: 405°

Question 2:

Which of the following angles is NOT coterminal with 120°?

Correct Answer: -120°

Question 3:

What is a positive coterminal angle of -30°?

Correct Answer: 330°

Question 4:

Which of the following radian measures is coterminal with π/2?

Correct Answer: 5π/2

Question 5:

A coterminal angle is defined as:

Correct Answer: An angle that shares the same terminal side

Question 6:

What is a negative coterminal angle of 70°?

Correct Answer: -290°

Question 7:

If an angle is 11π/6, what is a negative coterminal angle?

Correct Answer: -π/6

Question 8:

Which of the following angles cannot be found coterminal angles with each other?

Correct Answer: 1080°

Question 9:

An angle that is larger than one rotation of a circle will have more than 2 coterminal angles.

Correct Answer: True

Question 10:

Which value could not be used to find a coterminal angle?

Correct Answer: π

Fill in the Blank Questions

Question 1:

Coterminal angles share the same __________ side.

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 negative coterminal angle of 60° is __________.

Correct Answer: -300°

Question 5:

An angle of 7π/4 is coterminal with __________.

Correct Answer: -π/4

Question 6:

If an angle is 800°, you have to subtract 360° at least ____ to get a coterminal angle.

Correct Answer: 1

Question 7:

An angle can have an infinite number of __________ angles.

Correct Answer: coterminal

Question 8:

To get a positive coterminal angle, you need to _____ 360°.

Correct Answer: add

Question 9:

An angle of -700° is coterminal with _____.

Correct Answer: 20°

Question 10:

The unit circle relates angles and their __________ values.

Correct Answer: trigonometric

Educational Standards

PC.T.1.1:Draw and recognize angles in standard position using radian measure, and determine the quadrant of the terminal side. PC.T.1.9:Describe and analyze the relationships of the properties of a unit circle. PC.T.1.2:Convert radian measure to degree measure and vice-versa.

Teaching Materials

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