Radian Measure (Edexcel IGCSE Further Pure Maths): Revision Note

Radian Measure

What are radians?

• Radians are an alternative to degrees for measuring angles

• 1 radian is defined as the angle in a circle sector of radius 1 and arc length 1

• Radians are often given in terms of $\pi$

  • $2\pi$ radians = 360°

  • $\pi$ radians = 180°

• The symbol for radians is ^c but it is more usual to see rad

  • When $\pi$ is involved, no symbol for radians is needed

    • With $\pi$ it is obvious it is in radians

  • You should never omit the symbol for degrees

• In the exam a question will usually tell you which angle measure to use

  • But radians must be used if calculus with the trigonometric functions is involved

How do I convert between radians and degrees?

• Use $\pi$ radians = 180° to convert between radians and degrees

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

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

• Some of the common equivalents are:

  • $2\pi \mathrm{rad}=360°$

  • $\pi \mathrm{rad}=180°$

  • $\frac{\pi }{2}\mathrm{rad}=90°$

  • $\frac{\pi }{3}\mathrm{rad}=60°$

  • $\frac{\pi }{4}\mathrm{rad}=45°$

  • $\frac{\pi }{6}\mathrm{rad}=30°$

• It is useful to remember these and use them to work out other conversions

• Your calculator will be able to work with both radians and degrees