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Math Help - Cot/Arctan

  1. #1
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    Cot/Arctan

    Math homework is not going too well...

    1. cot (arctan [sq. rt.]3/x)


    Any and all help is appreciated. Thanks.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Cot/Arctan-capture.jpg

    I hope this is clear

    Good luck.
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  3. #3
    Junior Member teuthid's Avatar
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    two things you need to do this:
    1) \cot{x}=\frac{1}{\tan{x}}
    2) \tan [\tan^-1(x)]=x

    and so we have...

    \cot \left[ \tan^{-1} \left(\frac{\sqrt{3}}{x}\right) \right]

    <br />
=\frac{1}{\tan \left[ \tan^{-1} \left(\frac{\sqrt{3}}{x}\right) \right]}

    =\frac{1}{\frac{\sqrt{3}}{x}}

    =\frac{x}{\sqrt{3}}=\frac{\sqrt{3}x}{3}
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  4. #4
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    Hello, TheHardcoreDave!

    1)\;\cot\left[\arctan\left(\frac{\sqrt{3}}{x}\right)\right]

    We have: . \cot\underbrace{\left[\arctan\left(\frac{\sqrt{3}}{x}\right)\right]}_{\text{some angle }\theta}

    Then: . \theta \:=\:\arctan\left(\frac{\sqrt{3}}{x}\right)\quad\R  ightarrow\quad \tan\theta \:=\:\frac{\sqrt{3}}{x} \:=\:\frac{opp}{adj}


    \theta is in a right triangle with: opp = \sqrt{3},\;adj = x
    Code:
                            *
                         *  |
                      *     |  _
                   *        | √3
                *           |
             * θ            |
          * - - - - - - - - *
                   x

    Now . . . what is \cot\theta ?

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