IBMathsDPAnalysis & Approaches (AA)SLRevision Notes3. Geometry & TrigonometryGeometry ToolkitRadian Measure

Radian Measure (DP IB Analysis & Approaches (AA)): Revision Note

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Radian Measure

What are radians?

  • Radians are an alternative to degrees for measuring angles

  • Radians measure the length of the arc of the unit circle corresponding to the angle

  • The symbol c can be used to denote that the angle is in radians

    • Usually you do not use a symbol when working with radians

Diagram of a unit circle with radius 1, showing minor arc PQ, angle 1 radian (≈57.3°), and labels for minor and major arcs PQ.
The unit circle and radians

How do I convert between radians and degrees?

  • Use π radians = 180° to convert between radians and degrees

    • Multiply radians by begin mathsize 16px style 180 over straight pi end style to get degrees

    • Multiply degrees by begin mathsize 16px style straight pi over 180 end style to get radians

  • Radians are normally written as a multiple of π or as a decimal approximation

  • Here are some common conversions

Angle in degrees

Angle in radians

360°

2 straight pi

180°

straight pi

90°

1 half straight pi

60°

1 third straight pi

45°

1 fourth straight pi

30°

1 fourth straight pi

Examiner Tips and Tricks

In your exam you should use radians unless otherwise indicated.

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

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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.

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