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Math Help - trig four quadrants

  1. #1
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    trig four quadrants

    Hello everyone!

    I've found the answer to this just need to know if its in the right term

    Given that cosec θ = −2, tan θ = 1/3√3

    and −π < θ < π, find the exact
    value of the angle θ in radians. Justify your answer.

    answers are

    cosec = 1/sin = -1/2 (which means its in the 3rd or 4th quadrant)
    tan = 1/3√3 (which means its in the 1st or 3rd quadrant)

    this means that theta is in the 3rd quadrant

    but is it -1/6pi or -5/6pi? because each of their values is either +/- 1/6pi but surely that cant be right because -1/6pi is -30 which is not in the 3rd quadrant, could someone just classify this for me! cheers
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  2. #2
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    Re: trig four quadrants

    hi emakarov, sorry i don't think i explained very well,

    first off i meant (1/3) * √3 which i think is the same as what you wrote 1 / √3

    secondly i what i was trying to say was that both these values

    sinθ = -1/2 = -1/6pi and

    tanθ = 1/√3 = 1/6pi

    but this is where i get stuck, because i have two values which are either positive or negative of 1/6 pi and which are neither in the third quadrant so i thought it must be -5/6pi (-150 degrees)

    but this is where i need help
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  3. #3
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    Re: trig four quadrants

    hi skeeter, please explain further. many thanks
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  4. #4
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    Re: trig four quadrants

    Thanks for your help emakarov,

    That has cleared a lot of things up, looks like I'm going to have to study harder!!
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