Radian Measure (Edexcel A Level Maths) : Revision Note

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Radian Measure

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?

5-4-1-radian-measure-notes-diagram-6-new
  • The area of a sector is A = ½r2θ

5-4-1-radian-measure-notes-diagram-7-new

Solving problems with radians

  • Other angle, circle, area, etc skills may be needed

  • For example, area of a triangle "A = ½absinC"

-3H-5KJu_5-4-1-radian-measure-notes-diagram-8-new

Examiner Tips and Tricks

  • 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

Worked Example

Radian Measure Example Diagram 1, A Level & AS Level Pure Maths Revision Notes
5-4-1-radian-measure-example-diagram-2-ew
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Paul

Author: Paul

Expertise: Maths Content Creator (Previous)

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.

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