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Math Help - Please check that

  1. #1
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    Apr 2009
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    Please check that

    Can someone tell me the solution of following problems:
    1.
    (sin(pi/2 - x) - cos^3x)/(sin(2x + 4pi))

    My solution sinx/2


    2.
    I have to get other 2 values
    sinx=2/3
    _______
    sin2x = ?
    tan(pi/4-x) = ?

    3.
    y = x/5 - 1
    y = -5x/4 + 1


    k1 = 1/5
    k2 = -5/4


    tan()=|(k2-k1)/(1+k1*k2)|
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  2. #2
    Junior Member
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    Jan 2009
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    1.) Yes, assuming that you are supposed to simplify that expression, I'm also arriving at \frac{sinx}{2}.

    2.) Hmm, I think there's some information missing here. In order to evaluate sin2x, you could use the identity sin2x=2sinxcosx. Since you have the value of sinx, cosx can be found using sin^2x + cos^2x = 1 - but that gives two values for cosx, one positive and another negative. Usually, these type of questions will give a rage for the value of x, or make a comment such as "x is an acute angle", so that you can determine whether cosx is positive or negative.

    3.) Please be clearer. Specifically, tan() makes literally no sense.
    Last edited by Referos; April 13th 2009 at 12:06 PM. Reason: grammar
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  3. #3
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    2.) Lets say it is positive. For cosx I get square root of 5 divided by 3. For tanx I get 2 times square root of 5 divided by 5.

    Now I put this values to get sin2x (my solution is 4 times square root of 5 divided by 9) and to get tan(pi/4 - x), my solution to this is 1 - (2 times square root of 5 divided by 5) / 1 + (2 times square root of 5 divided by 5)

    3.) I ment tanφ

    and my solution is: 62 39'

    Thank you very much.
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