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A Math Problem

  1. Aug 13, 2006 #1
    A Math Problem....

    Hi Guys,

    I'm totally stuck on the following problem, if anybody could spare me some of their time to guide me through the solution that would be great.

    I have a screenshot of the problem on the following site...

    http://putfile.com/pic.php?pic=main/8/22412435578.jpg&s=f10
     
  2. jcsd
  3. Aug 13, 2006 #2

    0rthodontist

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    Step 1 is expand the series to 4 terms. Do you know what the 0th term is?
     
  4. Aug 13, 2006 #3
  5. Aug 13, 2006 #4

    0rthodontist

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    That looks correct. The one comment I have is that it is not legitimate to expand it like that, using all r's. If you use r in an expression, then wherever else the r appears in the expression, it has to mean the same thing--you can't have one group of r's be 0, the next be 1, and so on. You should just skip straight to the step where you substitute in the values.

    The next step is to check to see that it approximates the cosine. Calculate the cosine of some angle t and then evaluate that series of 4 terms where x = t.
     
  6. Aug 13, 2006 #5
    "The next step is to check to see that it approximates the cosine. Calculate the cosine of some angle t and then evaluate that series of 4 terms where x = t."

    How do I do this? This is the part I am unsure about.
     
  7. Aug 13, 2006 #6

    0rthodontist

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    let's say I have a series of 4 terms, x + x^2 + x^3 + 5x^4
    Now if I want to evaluate this series at x = 2, this is what I do:
    2 + 2^2 + 2^3 + 5*2^4
    = 2 + 4 + 8 + 160
    = 174

    You want to do a similar thing, but with an angle in radians.
     
  8. Aug 13, 2006 #7
    I'm trying but i'm not understanding what I should be seeing at the end of my calculations.
     
  9. Aug 13, 2006 #8

    0rthodontist

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    Well, what are your calculations?
     
  10. Aug 13, 2006 #9
    X = 5

    substitue:

    = 1 - (1/2x5^2) + (1/24x5^4) - (1/720x5^6)

    = 1 - 12.5 + 26.041666... - 21.7013888...

    = - 7.159722

    What does this mean? (My maths teacher was a Media teacher)
     
  11. Aug 13, 2006 #10

    0rthodontist

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    What that means is that using the approximation of the first four terms of the series, cos 5 = -7.16. This is clearly not true, but remember that it's only an approximation: it can be wrong. In fact the error increases as the absolute value of x increases. Try a smaller x, say x = 1, instead.
     
  12. Aug 13, 2006 #11
    X = 1

    substitue:

    = 1 - (1/2x1^2) + (1/24x1^4) - (1/720x1^6)


    = 1 - (0.5) + (0.041666..) - (0.0013888....)

    = 0.5402778

    ????
     
  13. Aug 13, 2006 #12

    0rthodontist

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    Now what's cos 1?
     
  14. Aug 13, 2006 #13
    0.999847695
     
  15. Aug 13, 2006 #14
    I think i had my calculator set in the wrong mode...

    I switched it to 'RAD'

    and it came up

    0.5403
     
  16. Aug 14, 2006 #15
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