Introduction to Radians and the Unit Circle

Karen Service, Oct 16, 2017

Introduction to what a radian is, and how the unit circle is created.

Table of Contents

  1. Review of Circumference and Diameter
    1. Relationship Between Circumference & Diameter
  2. Visualizing Radians
    1. Visualizing Radians and Arc Length
  3. Creating a Unit Circle
    1. Unit Circle Development - Part 1
    2. Unit Circle Development - Part 2
    3. Unit Circle Development - Part 3
  4. Completed Unit Circle
    1. Unit Circle - Degrees & Radians

1.

Review of Circumference and Diameter

  • 1. Relationship Between Circumference & Diameter

1.1.

Relationship Between Circumference & Diameter

– Karen Service

2.

Visualizing Radians

  • 1. Visualizing Radians and Arc Length

2.1.

Visualizing Radians and Arc Length

1. When the angle is set to 1 radian, what do you notice about the radius and arc length?
2. What is the relationship between arc length, the angle (in radians) and radius?
3. In a circle there are [math]360^\circ[/math]. How many radians is this?[br](Hint: think about arc length and circumference!)
– Karen Service

3.

Creating a Unit Circle

  • 1. Unit Circle Development - Part 1
  • 2. Unit Circle Development - Part 2
  • 3. Unit Circle Development - Part 3

3.1.

Unit Circle Development - Part 1

1. Set the angle to [math]45^\circ[/math]. What type of triangle is produced?
2. Use Pythagoras' Theorem to find the exact value of sides f and g (remember what type of triangle this is?).
– Karen Service

3.2.

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3.3.

–

4.

Completed Unit Circle

  • 1. Unit Circle - Degrees & Radians

4.1.

Unit Circle - Degrees & Radians

– Karen Service

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