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Arcs & Sectors Using Radians (DP IB Applications & Interpretation (AI)): Revision Note

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Arcs & Sectors Using Radians

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

  • As the radian measure for a full turn is 2 straight pi, the fraction of the circle becomes fraction numerator theta over denominator 2 pi end fraction

  • Working in radians, the formula for the length of an arc will become

l equals fraction numerator theta over denominator 2 pi end fraction blank cross times 2 pi space r

  • Simplifying, the formula for the length, l, of an arc is


    l space equals space r theta space

    • theta is the angle measured in radians

    • r is the radius

    • This is given in the formula booklet, you do not need to remember it

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

  • As the radian measure for a full turn is 2 straight pi, the fraction of the circle becomes fraction numerator theta over denominator 2 pi end fraction

  • Working in radians, the formula for the area of a sector will become

A equals fraction numerator theta over denominator 2 pi end fraction blank cross times pi space r squared

  • Simplifying, the formula for the area, A, of a sector is


    A equals 1 half space r squared space theta

    • theta is the angle measured in radians

    • r is the radius

    • This is given in the formula booklet, you do not need to remember it

Worked Example

A slice of cake forms a sector of a circle with an angle of straight pi over 6 radians and radius of 7 cm. Find the area of the surface of the slice of cake and its perimeter.

 

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    Amber

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    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.