Moving from Degrees to Radians: Conversion between Degrees and Radians YouTube Lecture Handouts

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Topics

  • What is a radian?
  • Advantages of Measuring and “Thinking” in Radians
  • Conversion from Radians to Degrees
  • Conversion from Degrees to Radians
  • Conversion Tables

What is a Radian?

  • Angle subtended by an arc at the center in radians is the ratio of arc length to radius.
  • 1 radian is the angle for which the arc length is one radius.
  • The circumference is π diameters and radii, so one complete revolution is radians.
  • Traditionally a circle was divided into 360 degrees since that number has a convenient list of factors, and so one radian is degrees.
Illustration: What is a Radian?

Always Think in Radians Not 360 Degrees

Illustration: Always Think in Radians Not 360 Degrees
  • Radian is most natural unit to measure angles.
  • Algebraic expansion of trigonometric functions. .
  • Calculus! !
Illustration: Always Think in Radians Not 360 Degrees

Degrees were used because 360 has lot of factors and so easy to divide the circle into equal portions

Converting from Radians to Degrees

  • radians = 360 degrees
  • 1 radian = degrees
  • 360 degrees radians
  • 1 degree = radians

Convert 90 degrees to radians.

Convert into degrees (30 degrees)

Convert -150 degrees to radians

Convert

Problem

In a circle with radius 6 cm, what is the measure (in degrees) of an arc whose length is cm

Some Common Conversions

Mayank