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Math Help - number of terms for approximation

  1. #1
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    number of terms for approximation

    given that sin(1) = 1 - 1/3! + 1/5! ... 1/(2i+1)! determin how many terms are needed to approximate sin(1) within 10^-4
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  2. #2
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    Quote Originally Posted by diroga View Post
    given that sin(1) = 1 - 1/3! + 1/5! ... 1/(2i+1)! determin how many terms are needed to approximate sin(1) within 10^-4


    5! = 120
    7! = 5040
    1/5040 = 0.0001984

    Therefore you need the next term:

    1/9! = 0.000002755
    That gives an approximate for the 10^{-4} value required.
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  3. #3
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    well yeah i can add up the values.

    sin(1) = 0.8414709848
    7 terms = 0.841468254
    9 terms = 0.8414710097

    it says to approximate with in 10^-4 which would be 0.8414. 7 terms looks good enough or by rounding do i need to go to 9 terms.

    Should there be a formula to solve this or is it just manul computation?
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