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Math Help - solving help required

  1. #1
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    solving help required

    hi.

    please help me to solve these equations

    A*sin(atan(2000/B)*2) = 500
    A*sin(atan(4000/B)*2) = 752.545

    and explain it.

    thanks
    mohanraj
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  2. #2
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    to add to that, by dividing the equation and by substitution method, we can find the value, but i dont know how to solve the equations.
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  3. #3
    MHF Contributor
    Joined
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    Quote Originally Posted by sanmo4 View Post
    hi.

    please help me to solve these equations

    A*sin(atan(2000/B)*2) = 500
    A*sin(atan(4000/B)*2) = 752.545

    and explain it.

    thanks
    mohanraj
    Umm, big numbers.

    You know that arctan(U) is an angle.
    It is an angle whose tan value is U.
    So, in its reference triangle,
    opposite side = U
    adjacent side = 1
    hypotenuse = sqrt(1 +U^2)
    And then, sin(arctan(U)) = opp/hyp = U /sqrt(1 +U^2)
    And, cos(arctan(U)) = adj/hyp = 1 /sqrt(1 +U^2)

    To avoid plunging into very large numbers at once, let
    arctan(2000/B) = angle X
    arctan(4000/B) = angle Y

    Thus, the original equations can be re-written as:
    A*sin(2X) = 500 ---------(1a)
    A*sin(2Y) = 752.545 ------(2a)

    Spread those:
    A[2sinXcosX] = 500 ---------(1b)
    A[2sinYcosY] = 752.545 -----(2b)

    To eliminate A, divide (1b) by (2b)
    sinXcosX /sinYcosY = 0.664412 -------------(3)

    Use the method in the sample U above and you'd get
    sinX = 2000 /sqrt(B^2 +4,000,000)
    cosX = B /sqrt(B^2 +4,000,000)

    sinY = 4000 /sqrt(B^2 +16,000,000)
    cosY = B /sqrt(B^2 +16,000,000)

    Substitute those into Eq.(3)
    Etc....

    You should get B = 5700
    And A = 800
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  4. #4
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    thanks for your reply... thanks for your explanation. the answer am getting by substitution also same..
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