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Require help understanding small angle approximation

  1. Sep 3, 2012 #1
    1. The problem statement, all variables and given/known data
    I was recently given this question and very little explanation of the concept. I've struggled with this for a week and read absolutely everything I can find and I'm still not any closer to understanding it. Can anyone please point me in the right direction or explain how to do question 1) and 2)? There are many more questions, but if I can get 1) and 2) down then I should be able to answer the rest by myself. I appreciate any help.

    2. Relevant equations
    Unsure


    3. The attempt at a solution
    Unsure
     
  2. jcsd
  3. Sep 3, 2012 #2
    The equation at the end explains that |sinθ-θ|/|sinθ| gives the error in approximating sinθ by θ. In other words, it gives the percentage which theta differs from sinθ.

    The first question asks: For what values of theta does theta differ from sinθ by less than 5%? in other words:
    [itex]\displaystyle \frac{|sinθ-θ|}{|sinθ|}≤.05[/itex]
     
  4. Sep 3, 2012 #3

    Thank you, I had been using the equation incorrectly without realising. I have the correct answers now.
     
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