Subject: Trig question If x is in radians, how do you solve for x, where: xsin(x) = constant?
Keith Roble I know of no way to directly solve this equation, the best you can do is approximate a solution. The most widely used technique is Newton's method, or sometimes called the NewtonRaphson method. This technique applies to equations of the form f(x) = 0 where f(x) is a differentiable function and requires the function f(x) and its derivative f'(x). The procedure progresses through a seuqence of steps.
In many situations the sequence x_{1}, x_{2}, x_{3}, ... will converge to a solution of the equation f(x) = 0. For your problem suppose that the constant is C and then the equation xsin(x) = constant can be written f(x) = 0 where Here, f'(x) = 1 + cos(x) and the iterative step is given by I tried this technique with C = 10 and x_{1} = 10 with the following results
You need be careful when applying Newton's method. In particular it is sensitive to the initial approximation x_{1}. For some values of x_{1} the sequence may not converge, or may converge to a solution which is different from the solution you are seeking. I suggest that you find a reference on Newton's method. You can find it in most Calculus books. Cheers,Harley
