Expert: David Hemmer - 8/29/2007

Question
hi how do i know that i have found all the positive roots of a function such as the one given below:
   x-1-2*sin(pi*x)=0

Answer
This equation is

x=1+2sin(Pi*x)

First of all notice that sin of anything is always between -1 and 1. Thus the right hand side of your equation is always between 0 and 3. Thus there are no solutions except those between 0 and 3. You might try sketching neatly the graphs of x and 1+2sin(pix) to see where they intersect, if you haven't found the solutions between 0 and 3.