Solve the equation x-sinx=0. Solution In order to solve the equation, which is a transcedental one, you have to find the derivative of the function f. Yes, we can find the derivative of the function f, because is a continuous function, formed by elementary functions as the linear one,x , and the trigonometrical one, sin x! f\'(x)=1-cosx We can note that is a monotone increasing function ( -10 =>f(x)>0, so f(x) is an injection. We can also do a very simple calculus: f(0)=0-sin0=0-0=0. We\'ve demonstrated earlier before that f(x) is an injection, so, x=0 is the only solution for x- sinx=0.