Radian Measure (Cambridge (CIE) O Level Additional Maths): Revision Note

Radian measure

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 $\frac{180}{\mathrm{\pi }}$

  • To convert from degrees to radians multiply by $\frac{\mathrm{\pi }}{180}$

• Some of the common conversions are:

  • $2\mathrm{\pi }{}^c=360°$

  • ${\mathrm{\pi }}^c=180°$

  • ${\frac{\mathrm{\pi }}{2}}^c=90°$

  • ${\frac{\mathrm{\pi }}{3}}^c=60°$

  • ${\frac{\mathrm{\pi }}{4}}^c=45°$

  • ${\frac{\mathrm{\pi }}{6}}^c=30°$

• It is a good idea to remember some of these and use them to work out other conversions