Radian Measure (CIE A Level Maths: Pure 1)

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

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 – one of the many reasons he is excited to be a member of the SME team.