System of measurement of angles

Angles are geometric figures formed by two rays that share a common endpoint, known as the vertex. The measurement of angles is crucial in various fields such as geometry, physics, engineering, and astronomy. There are two primary systems of measurement for angles: the Degree System and the Radian System.

1. Degree System:

  • Definition: The degree is the most common unit of measurement for angles.

  • Symbol: °

  • Full Circle: A full circle contains 360 degrees.

  • Subdivisions:

    • Minute: 1 degree is divided into 60 minutes (1° = 60').
    • Second: 1 minute is further divided into 60 seconds (1' = 60").
  • Example:

    • An angle of 45 degrees is written as 45°.
    • An angle of 30 degrees, 15 minutes is written as 30° 15'.

2. Radian System:

  • Definition: The radian is another unit of angular measure, often used in advanced mathematics and physics.

  • Symbol: rad

  • Full Circle: A full circle is equal to 2π radians (approximately 6.283 radians).

  • Relationship: 1 radian=180π.

  • Conversion:

    • To convert degrees to radians: Radians=(π180)×Degrees.
    • To convert radians to degrees: Degrees=(180π)×Radians.
  • Example:

    • An angle of π4 radians is equivalent to 45 degrees.

Choosing Between Degree and Radian:

  • Degrees are often used in everyday situations and basic geometry.
  • Radians are frequently used in calculus, physics, and advanced mathematical contexts due to their natural connection with the unit circle.