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Math Help - Solve for the indicated variable:

  1. #1
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    Solve for the indicated variable:

    cos^2x+3cos^2x+2=0 How do you solve this?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Solve for the indicated variable:

    If you wright:
    \cos^2(x)+3\cos^2(x)+2=0 \Leftrightarrow 4\cos^2(x)=-2 \Leftrightarrow \cos^2(x)=\frac{-1}{2}

    What do you notice?
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  3. #3
    Super Member TheChaz's Avatar
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    Re: Solve for the indicated variable:

    Quote Originally Posted by CprlCaboose View Post
    cos^2x+3cos^2x+2=0 How do you solve this?
    There might be a typo... (and yes, I have sobered-up since this morning!)

    cos^2(x) + 3cos(x) + 2 = 0 implies

    (cosx + 2)(cosx + 1) = 0
    ...
    Only in case of typo!
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  4. #4
    Junior Member PythagorasNeophyte's Avatar
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    Re: Solve for the indicated variable:

    cos^2 x + 3 cos^2 x+2=0

    4 cos^2 x = -2

    cos^2 x = -1/2

    cos x = plus or minus -1/2

    x lies in the 1st, 2nd, 3rd and 4th quadrant since it has positive and negative values. Now find the basic angle \alpha and solve for the 4 possible angles.
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: Solve for the indicated variable:

    Quote Originally Posted by PythagorasNeophyte View Post
    cos^2 x = -1/2

    cos x = plus or minus -1/2
    That's not true, if the equation was:
    \cos^2(x)=\frac{1}{4}
    Then you were right, because then:
    \cos(x)=\pm \frac{1}{2}

    Also, look at the graph of the function 4\cos^2(x)+2:
    http://www.wolframalpha.com/input/?i=4cos^2%28x%29%2B2

    What do you notice?
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