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Math Help - Value of cosec

  1. #1
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    Value of cosec

    Excuse the silliness of this question. It's been a wee while since I've done maths and I think I've forgotten something really basic.

    Anyway, I've got to find the value of y= - cosec^2(pi.x) where x = 1/3

    So far, I've gotten down to:

    = - 1/sin(60)

    Which, when banged into the calculator, = 1/ (square root)3/2 [if that makes sense].

    But, I'm conscious of the squared sign in the cosec. Does that mean anything?
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  2. #2
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    Quote Originally Posted by scofield131 View Post
    Excuse the silliness of this question. It's been a wee while since I've done maths and I think I've forgotten something really basic.

    Anyway, I've got to find the value of y= - cosec^2(pi.x) where x = 1/3

    So far, I've gotten down to:

    = - 1/sin(60)

    Which, when banged into the calculator, = 1/ (square root)3/2 [if that makes sense].

    But, I'm conscious of the squared sign in the cosec. Does that mean anything?
    cosec^2(\pi \, x) = \frac{1}{sin^2(\pi \, x)}

    As you rightly mentioned sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}

    Therefore it becomes \frac{1}{\left(\frac{\sqrt3}{2}\right)^2}

    I got an overall answer of \frac{2}{3}
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  3. #3
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    That makes sense. Thanks :]
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  4. #4
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    sorry double post....
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  5. #5
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    Quote Originally Posted by e^(i*pi) View Post
    cosec^2(\pi \, x) = \frac{1}{sin^2(\pi \, x)}

    As you rightly mentioned sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}

    Therefore it becomes \frac{1}{\left(\frac{\sqrt3}{2}\right)^2}

    I got an overall answer of \frac{2}{3}

    the last one (result), i think it should be \frac{4}{3}
    since \frac {1}{\left(\frac{\sqrt3}{2}\right)^2} =\left (\frac{2}{\sqrt3}\right)^2 =\frac{4}{3}
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