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Math Help - Polynomial approximation

  1. #1
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    Polynomial approximation

    Here's a challenge: for the function y= a\,\sin{(bx+c)} + d, find a polynomial of degree 3 (ie a cubic) approximation for y on the interval from one trough to one peak (about the main original point of inflection) - eg for y=\sin{(x)} that interval would be \left[-\frac{\pi}{2}, \,\frac{\pi}{2}\right]

    Express the answer in the form y = px^3+qx^2+rx+s, where p, q , r and s are in terms of a, b, c and d.
    Last edited by nzmathman; April 20th 2009 at 07:04 PM.
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  2. #2
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    It doesnt seem to work when c \neq 0 I have no idea why?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by nzmathman View Post
    Here's a challenge: for the function y= a\,\sin{(bx+c)} + d, find a polynomial of degree 3 (ie a cubic) approximation for y on the interval from one trough to one peak (about the main original point of inflection) - eg for y=\sin{(x)} that interval would be \left[-\frac{\pi}{2}, \,\frac{\pi}{2}\right]

    Express the answer in the form y = px^3+qx^2+rx+s, where p, q , r and s are in terms of a, b, c and d.
    What is the norm against which the quality of the fit between the polynomial and function is to be judged?

    CB
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  4. #4
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    Hi, basically you find the approximation using certain points of the sine curve so that there is exactly enough to solve for a, b, c and d. (this is giving it away a bit but I used the point of inflection and one of the stationary points). Never mind my earlier post about it not working when c was not zero, I made a mistake in the formula but fixed it now
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