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Pure 4. Circular Measure

A Level Mathematics 9709 Examinations 2023 – 2025 Pure 1

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Why do we study it?

  • Where did 360 come from? No one knows for sure :)
    • Astronomers: the Earth revolves around the Sun in 360 days?
    • Ancient Babylonians: divided a circle into 6, then each angle into 60 more angles
  • Radians: simplifies formulae and calculations

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1. Radians

  • An arc equal in length to the radius of a circle subtends an angle of 1 radian at the centre
  • 2π radians = 360°
  • π radians = 180°

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  • * usually omit the word ‘radians’

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2. Length of an Arc

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3. Area of a Sector

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