Edexcel A Level Maths: Pure

Revision Notes

5.4.1 Radian Measure

A Level Only

Radian measure

  • Radians are an alternative to degrees for measuring angles

 
Radian Measure Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes
 

  • 1 radian is the angle in a sector of radius 1 and arc length 1
  • Radians are normally quoted in terms of π
  • This leads to
    • 2π = 360°
    • π = 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 obviously in radians)

  • Radians are used in trigonometry (see Exact Values) and calculus (First Principles Differentiation – Trigonometry)

 

How do I change between radians and degrees?

  • The most common are below, these are helpful to know

 
Radian Measure Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes
 

  • Multiples of these are quite common too, eg ¾π = 135°
  • For less familiar angles use π = 180° to convert

 
Radian Measure Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes
 
 

How do I use radians to find the length of an arc?

Radian Measure Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes
 
 

  • The length of an arc is s = rθ

 
Radian Measure Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes
 
 

How do I use radians to find the area of a sector?

Radian Measure Notes Diagram 6, A Level & AS Level Pure Maths Revision Notes
 
 

  • The area of a sector is A = ½θr2

 
Radian Measure Notes Diagram 7, A Level & AS Level Pure Maths Revision Notes
 

Solving problems with radians

  • Other angle, circle, area, etc skills may be needed
  • For example, area of a triangle “A = ½absinC”


Radian Measure Notes Diagram 8, A Level & AS Level Pure Maths Revision Notes

Exam Tip

  • Exam papers will have a mixture of questions in degrees and radians
  • Check the mode (degrees/radians) of your calculator before using it
  • Ensure you know how to change the mode on your calculator
  • For the Casio fx-991EX Classwiz
    • SHIFT then MENU SETUP
    • Choose option 2: ANGLE UNIT
    • Choose either 1: DEGREE or 2: RADIAN

 

Radian Measure Exam Tip Diagram 1, A Level & AS Level Pure Maths Revision Notes

Radian Measure Exam Tip Diagram 2, A Level & AS Level Pure Maths Revision Notes

Radian Measure Exam Tip Diagram 3, A Level & AS Level Pure Maths Revision Notes

 

A Level Only

Worked Example

Radian Measure Example Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

Radian Measure Example Diagram 2, A Level & AS Level Pure Maths Revision Notes

Close

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now