Thread: -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=-tan(x)

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=-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 , but they can only be approximated.

-Dan