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Math Help - Find cot(x)

  1. #1
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    Find cot(x)

    Function: csc(x)=-2
    Quadrant: 4
    find cot.

    Anyone? Last question of the year.
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  2. #2
    Super Member bigwave's Avatar
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    Cool

    Quote Originally Posted by BeSweeet View Post
    csc(x)=-2
     <br />
\frac{1}{sinx} = -2<br />

     <br />
-2sinx = 1<br />

     <br />
sinx = -\frac{1}{2}<br />

     <br />
sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6}<br />

    easy to get cotx from this

    since cosx(-\frac{\pi}{6}) = -\frac{\sqrt{3}}{2}
    and cotx is \frac{adj}{hyp} then cotx is just  <br />
-\sqrt{3}
    Last edited by bigwave; December 14th 2009 at 10:32 AM. Reason: getting cotx
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by BeSweeet View Post
    Function: csc(x)=-2
    Quadrant: 4
    find cot.

    Anyone? Last question of the year.
    Hi BeSweet,

    Last question? Wow. Have a very merry Christmas.

    \csc x = \frac{1}{\sin x}=-2

    \sin x = -\frac{1}{2}

    Use r^2=x^2+y^2 to find x.

    \sin x =\frac{y}{r}=-\frac{1}{2}

    y = -1, r = 2

    2^2=x^2+(-1)^2

    x=\sqrt{3}

    \tan x=\frac{y}{x}

    \cot x = \frac{1}{\tan x}=\frac{x}{y}=\frac{\sqrt{3}}{-1}=-\sqrt{3}
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