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Math Help - -tan(x)=x

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    -tan(x)=x

    I have the equation -tan(x)=x.
    I have no idea how to solve it.
    The above comes from the derivative of x*sin(x), which is x*cos(x)+sin(x). If we try to find the extremums of x*sin(x) we have:
    x*cos(x)+sin(x)=0
    <br />
x=-\frac {sin(x)}{cos(x)}<br />
    x=-tan(x)
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    Quote Originally Posted by fobos3 View Post
    I have the equation -tan(x)=x.
    I have no idea how to solve it.
    The above comes from the derivative of x*sin(x), which is x*cos(x)+sin(x). If we try to find the extremums of x*sin(x) we have:
    x*cos(x)+sin(x)=0
    <br />
x=-\frac {sin(x)}{cos(x)}<br />
    x=-tan(x)
    There is no algebraic/trigonometric way to solve it, but note that x = 0 is a solution. By graphing you should be able to see there are two more for 0 < x < 2 \pi, but they can only be approximated.

    -Dan
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