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Math Help - solving "X" in trig equation

  1. #1
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    solving "X" in trig equation

    This is my problem:
    (image looks funky on here so url provided)
    LaTeX:
    http://rogercortesi.com/eqn/tempimagedir/eqn9167.png
    solving "X" in trig equation-eqn9167.png

    My line of thinking is shown but the result makes no sense to me. My result just does not seem correct. Can someone show me my error?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: solving "X" in trig equation

    What do you not understand? Because I can't see any mistake ...
    Calculate the discriminant and afterwars do the back-substitution.
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    Re: solving "X" in trig equation

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  4. #4
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: solving "X" in trig equation

    Quote Originally Posted by Bowlbase View Post
    First, you mustn't write \cos=x , you should write \cos{\4\theta}=x .

    Now, after you solved your quadratic equation you got two roots.

    One root is \frac{1}{2}(-1-\sqrt{3}), and the second root is \frac{1}{2}(\sqrt{3}-1).

    Now you wrote:

    2x^2+2x-1=0=\frac{1}{2}(-1-\sqrt{3}), tell me how it is possible?!

    That is wrong!

    What you can write is the following:


    2x^2+2x-1=(x-\frac{1}{2}(-1-\sqrt{3}))(x-\frac{1}{2}(\sqrt{3}-1))

    If we return back to origins, we get:


    \cos{4\thete}=\frac{1}{2}(-1-\sqrt{3}) \approx -1.3

    It is impossible!

    So we left only with:

    \cos{4\thete}=\frac{1}{2}(\sqrt{3}-1)

    So, why you took the Arcsin from both sides?
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  5. #5
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    Re: solving "X" in trig equation

    gah, don't know why I used arcsin all of a sudden.

    let me rewrite this:

    http://rogercortesi.com/eqn/tempimagedir/eqn9167.png


    I dont know how to do the little +/- in LaTeX so I just split them with division symbol.

    The answer is looking for all values between 0-360 degrees. I just didn't type all that out.
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  6. #6
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: solving "X" in trig equation

    Quote Originally Posted by Bowlbase View Post
    gah, don't know why I used arcsin all of a sudden.

    let me rewrite this:

    http://rogercortesi.com/eqn/tempimagedir/eqn9167.png


    I dont know how to do the little +/- in LaTeX so I just split them with division symbol.

    The answer is looking for all values between 0-360 degrees. I just didn't type all that out.
    So, 0=\frac{1}{2}(-1\pm\sqrt{3}) ?

    Is the above looks right to you?!
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  7. #7
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    Re: solving "X" in trig equation

    I didn't mean to put 0= 1/2(-1+/-sqrt[3]). should be x. I just didn't put an x in the next line.

    http://rogercortesi.com/eqn/tempimagedir/eqn9167.png
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