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Math Help - More Trig

  1. #1
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    More Trig

    Hi,

    I'm lost on how to do part b) of the following question:

    More Trig-screen-shot-2010-06-25-11.13.57.png

    can anyone help?

    Explanation is needed! =) Thanks
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  2. #2
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    First thing I would do is take the sine of both sides, and use the addition of angles formula on the RHS.
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  3. #3
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    Quote Originally Posted by Ackbeet View Post
    First thing I would do is take the sine of both sides, and use the addition of angles formula on the RHS.
    Ok, so I've got:

    sin (arcsin(1-2x)) = sin(pi/3) - sin(arcsin(x))
    using the triangle rule from yesterday
    it simplifies to: 1-2x = 0.5 - x
    so x = 0.5

    but the restriction requires x to be less than 0.5?
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  4. #4
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    The RHS does not simplify as you have indicated. You have to use the addition of angles formula.

    [EDIT] Also, don't forget the Commandments of Algebra.
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  5. #5
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    Quote Originally Posted by Ackbeet View Post
    The RHS does not simplify as you have indicated. You have to use the addition of angles formula.

    [EDIT] Also, don't forget the Commandments of Algebra.
    oh yeah sorry.

    So its:

    1-2x = sin(pi/3)cos(arcsinx) - cos(pi/3)sin(arcsinx)
    1-2x = √3/2.(√(1-x^2)) - 0.5x

    then i get:

    12x^2 -12x +1 = 0

    is it right up to there? then i can just use x= -b +/- .....
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  6. #6
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    Yeah, you skipped a few steps, but I would agree with your conclusion. You do need to be careful: in squaring the equation to end up with your quadratic, you may have introduced spurious solutions. So you should definitely double-check against your allowed x's. Good work!
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  7. #7
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    Thanks! I've gotten through this one now =)

    Soon I'll have a few more worries! ^^
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  8. #8
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    You're welcome! Have a good one.
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