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IBMaths: AI HLDPRevision Notes3. Geometry & Trigonometry3.1 Geometry Toolkit3.1.2 Radian Measure

Radian Measure (DP IB Maths: AI HL)

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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

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

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 begin mathsize 16px style 180 over straight pi end style
    • To convert from degrees to radians multiply by begin mathsize 16px style straight pi over 180 end style
  • Some of the common conversions are:
    • begin mathsize 16px style 2 straight pi space to the power of c space equals space 360 space degree end style
    • begin mathsize 16px style straight pi to the power of space c end exponent space equals space 180 space degree end style
    • begin mathsize 16px style straight pi over 2 to the power of c space equals space 90 space degree end style
    • begin mathsize 16px style straight pi over 3 to the power of c space equals space 60 space degree end style
    • begin mathsize 16px style straight pi over 4 to the power of c space equals space 45 space degree end style
    • begin mathsize 16px style straight pi over 6 to the power of space c end exponent space equals space 30 space degree end style
  • It is a good idea to remember some of these and use them to work out other conversions
  • Your GDC will be able to work with both radians and degrees

5-4-1-radian-measure-notes-diagram-2

Examiner Tip

  • Sometimes an exam question will specify whether you should be using degrees or radians and sometimes it will not, if it doesn't it is expected that you will work in radians
  • If the question involves π then working in radians is useful as there will likely be opportunities where you can cancel out π
  • Make sure that your calculator is in the correct mode for the type of angle you are working with

Worked example

i)
Convert 43.8° to radians.

aa-sl-3-1-2-radian-measure-we-solution-part-i

 

ii)   Convert  fraction numerator 5 straight pi over denominator 4 end fraction to degrees.

aa-sl-3-1-2-radian-measure-we-solution-part-ii

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    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.