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A level - Small angles

Discussion in 'Mathematics' started by icosahedron, Oct 2, 2019.

  1. icosahedron

    icosahedron New commenter

    Edexcel (see page 140 of the Pearson pure mathematics book 2 challenge part b) seem to think that if theta is small then 4theta is also small, it is just me that thinks this is nonsense. I can imagine smart maths students getting into knots with this unless pre-warned, I hope they don't put a question like this in the exam.
     
    Last edited: Oct 2, 2019
  2. gainly

    gainly Lead commenter

    There was an even worse example in a question I did with one of my students, I think it was MEI. The question involved using the small angle approximation to solve an equation and then commenting on the validity. The answer was theta = 0.1 or 5. The mark scheme said 0.1 was valid as it is small but not 5. This might have been just about OK except the question involved 5(theta) and 10(theta).
     
  3. CHuynh

    CHuynh New commenter

    "theta is small hence 4 theta is small" is assuming that "theta approaches zero indefinitely" which is the concept of small angle. Without this concept, there is no guarantee that "4theta" will be small enough for the purpose. I believe there needs to be a clear definition of what values can be accepted as "small" if values are to be used in a test and its marking scheme.
     
  4. gainly

    gainly Lead commenter

    If the approximations are applied as the limit as theta approaches zero, then it would be fine to use them for 5theta or 10theta.

    Clearly it doesn't make much sense in the example I gave where theta = 0.1, so 10theta = 1. Sin(1) = 0.841, and tan(1) = 1.557 so the approximation isn't even close.
     

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