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How do i find the value of cos(theta)

  1. Nov 13, 2006 #1
    How do i find the value of cos(theta) if theta was given as 75(+/-)5?

    Ans:____(+/-)_____.

    How do i even start with this? How do i find the uncertainty of cos (theta)? Do i use the uncertainty of theta or the fractional uncertainty? Or do i just find cos 80, cos 75 and cos 70 and then find the uncertainty by deducing it from the found values/.?

    Any help will truly be appreciated. Thanks.
     
    Last edited: Nov 13, 2006
  2. jcsd
  3. Nov 13, 2006 #2

    nrqed

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    You use a Taylor expansion.
    The result is that
    [tex]
    cos (\theta \pm \delta \theta) \approx cos(\theta) \pm (\delta \theta) ~sin(\theta)[/tex]
    where you must use [itex] \delta \theta [/itex] in radians .

    Hope this helps.

    Patrick
     
  4. Nov 13, 2006 #3
    Hi, thanks for the help.. But one qn though. What will the value of [tex](\delta \theta) [/tex] be? Is it 5? But i though for this to apply, ur change has gotta be small? i calculated the value of [tex](\delta \theta) ~sin(\theta)[/tex] and it is very big? Even bigger than the real value?
     
    Last edited: Nov 13, 2006
  5. Nov 13, 2006 #4

    OlderDan

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    [tex](\delta \theta) [/tex] has to be in radians. It would not be 5. Even so, it is possible for the uncertainty to be bigger than the value. For θ very near 90°, cos(θ) is near zero and sin(θ) is nearly 1, so the error would be about [tex](\delta \theta) [/tex], which could easily be bigger than cos(θ) even when expressed properly in radians.
     
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