Radian Measure (Cambridge O Level Additional Maths)

What are radians?

• Radians are an alternative to degrees for measuring angles
• 1 radian is the angle in a sector of radius 1 and arc length 1
  • A circle with radius 1 is called a unit circle
• Radians are normally quoted in terms of π
  • 2π radians = 360°
  • π radians = 180°
• The symbol for radians is ^c but it is more usual to see rad
  • Often, when π is involved, no symbol is given as it is obvious it is in radians
  • Whilst it is okay to omit the symbol for radians, you should never omit the symbol for degrees
• In the exam you should use radians unless otherwise indicated

Definition of a radian using a unit circle

How do I convert between radians and degrees?

• Use π ^c = 180° to convert between radians and degrees
  • To convert from radians to degrees multiply by 
  • To convert from degrees to radians multiply by 
• Some of the common conversions are:
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• It is a good idea to remember some of these and use them to work out other conversions