Lecture 5.1: Angles

Introduction to Angles, Lines, and Rays

• Ray: A line with a starting point that extends infinitely in one direction.
  • Example: Ray A, denoted with an arrow going in one direction.
• Line: Extends infinitely in both directions.
  • Example: Line AB.

Angle Measure

• Positive Angle Measure: When moving counterclockwise from the initial side to the terminal side.
• Negative Angle Measure: When moving clockwise from the initial side to the terminal side.
• More than Full Rotation: When an angle is more than 360 degrees.

Standard Position of an Angle

• An angle theta is in standard position if:
  1. Its vertex is at the origin of a rectangular coordinate system.
  2. Its initial side coincides with the positive x-axis.
• Counterclockwise Movement: Positive angle (Theta is positive).
• Clockwise Movement: Negative angle (Theta is negative).

Central Angle

• A central angle is positive and its vertex is at the center of the circle.
• Types of central angles:
  • Angle with terminal side in Quadrant 2.
  • Quadrantal Angle: Terminal side is on an axis, not in a quadrant.

Common Angle Measures

• Full Rotation: 360 degrees.
• Half Rotation: 180 degrees (half of 360).
• Quarter Rotation: 90 degrees (half of 180).
• Eighth Rotation: 45 degrees (half of 90).

Correction on Rotations

• Two Rotations: 720 degrees.
• Three Rotations: 1080 degrees.
• Four Rotations: 1440 degrees.

Common Angles

• Right Angle: 90 degrees.
• Straight Angle: 180 degrees, forming a straight line.