# Math Help - -tan(x)=x

1. ## -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
$
x=-\frac {sin(x)}{cos(x)}
$

x=-tan(x)

2. Originally Posted by fobos3
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
$
x=-\frac {sin(x)}{cos(x)}
$

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