Is there an analytical solution to sin (pi*x) =pi*x?

Answer 1

Of course there is a solution. If you draw y = sin(pi*x). You'll note that at x=0, y is 1 and at x= 1/2, y=0. So the graph goes from 1 to 0.

Now look at y=pi*x. When x=0, y=0 and when x=1/2, y=pi/2=1.57. So the line goes from 0 to 1.57. How can the two curves miss one another? Answer--they can't