1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Linear Approximations and Differentials
  1. Linear Maps (Replies: 0)

Loading...