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Homework Help: Linear Approximations and Differentials

  1. Oct 27, 2006 #1
    Alright I just did the following question, and was hoping I did it right:

    Use differentials(or, equivalently, a linear approximation) to estimate the given number)

    cos 31.5* (* meaning degrees)

    f(x) = cosx
    f(31.5*) = ?

    a is chosen to be the closest number to the number evaluating in the function of, such that the equation can be easily evaluated.
    a= 30*, then dx = 31.5*-30*= 1.5*

    delta y is approximately equal to dy
    delta y = f(31.5*)-f(30*)
    = cos31.5* - cos30*
    = cos31.5* - root3/2

    dy = f'(30*)dx

    f'(x) = -sinx -> f'(30*) = -sin(30*) = -0.5

    dy = (-1/2)(1.5*) = -1/2(pi/120) = -(pi)/240

    Hence: cos31.5* - root3/2 is approximately equal to -(pi)/240 or:
    cos(31.5*) = root3/2 - (pi)/240

    I'm just checking to see if I followed the correct steps in solving this question. Thanks guys.
  2. jcsd
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