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Math Help - Using sin,cos,tan formulas.

  1. #1
    Member classicstrings's Avatar
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    Using sin,cos,tan formulas.

    I have v = 1000sin@cos@tan(@/2)
    and I need to rearrnge it to

    v = asin^2(@) + bsin^4(@/2)
    And hence find values a and b.

    Tried using double angle formulas, but I'm having trouble. Thanks for the help!
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  2. #2
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    Hello, classicstrings!

    Is there a typo?
    In the final form, aren't both angles ½θ ?


    I have: .v .= .1000·sinθ·cosθ·tan(½θ)

    and I need to rearrange it to: .v .= .a·sin²(½θ) + b·sin^4(½θ)

    And hence find values a and b.

    Identities
    . - - . sinθ .= .2·sin(½θ)·cos(½θ)
    . . . . cosθ .= .1 - 2·sin²(½θ)
    . .tan(½θ) .= .sin(½θ)/cos(½θ)


    We have: .v .= .1000 · sinθ · cosθ · tan(½θ)

    . . . . . . . .v .= .1000 · 2·sin(½θ)·cos(½θ) · (1 - 2·sin²θ) · sin(½θ)/cos(½θ)

    . . . . . . . .v .= .2000·sin²(½θ)·(1 - 2·sin²θ)

    . . . . . . . .v .= .2000·sin²(½θ) - 4000·sin^4(½θ)


    Therefore: .a = 2000, b = 4000



    Edit: silly me . . . I had dropped a zero . . . sorry!
    Last edited by Soroban; March 15th 2007 at 03:02 PM.
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  3. #3
    Member classicstrings's Avatar
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    My error in forgetting the @/2.

    Is there any chance that there is an error in your working?

    I think you left out one zero in 1000, so a = 2000, and doesn't b = negative 4000? Thanks!
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