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Small Angle Approximation

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    Find, by comparison with exact trigonometry, the angle,  (provide a numerical value
    in degrees), above which the small angle approximation departs from the exact result by more than 1 percent.


    2. Relevant equations

    Approx.: d = s = rθ
    Exact: d = 2*r*Sin(θ/2)

    3. The attempt at a solution

    .01 = |Exact - Approx.|/Exact

    (θ/2)*Csc(θ/2) = 1.01


    At this point I am unsure of how to isolate for θ. Any tips are greatly appreciated, thanks!
     
  2. jcsd
  3. Jan 15, 2013 #2

    SammyS

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    That equation can only be solved numerically or graphically.

    Don't forget to change the angle to degree measure.
     
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