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Math Help - General solution using reciprocal identities

  1. #1
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    General solution using reciprocal identities

    Ok, I can't figure out how to do this. I understand that you treat this like X^(2)+ X+1 and I can get to the point where you find what cos is equil to, but when puting the unit circle vallues is where im confused. Ok I have recently swiched to schools because I just had surgery so I couldnt be around that many people at a time. My other teacher told us we could not have decimal answers in this unit and in this new book I got there is decimal answers in it. I have no idea how to get the decimal answers. So here is the question Im trying to figure out.

    Solve the equation algibraically over the domain 0<X<2pie: sec^(2)X + 5secX+ 6=0

    This is my work, please tell me if im doing anything wrong
    (sec+3)(sec+2)=0
    secX=-3 secX=-2
    1/(cos -3) 1/(cos -2)
    cos= -1/3 cos=-1/2

    2pie/3, 4pie/3...
    So, now how do I get the decimal answers?
    The book say the answers are 4pie/3, 2pie/3, 4.37, 1.91
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  2. #2
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    Re: General solution using reciprocal identities

    \cos{x} = -\frac{1}{2} is a unit circle value ... x = \frac{2\pi}{3} , x = \frac{4\pi}{3}

    \cos{x} = -\frac{1}{3} has two solutions, one in quad II and one in quad III

    x = \arccos\left(-\frac{1}{3}\right) gives the solution in quad II

    x = 2\pi - \arccos\left(-\frac{1}{3}\right) gives the quad III solution


    btw, this is pi ...



    and this is pie ...

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  3. #3
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    Re: General solution using reciprocal identities

    lol, ok thankyou.
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