I’m not a math major, but I think I know the answer to this.
Sine is modeled using a unit circle. That’s basically a circle drawn on an X and Y plane with the origin at (0,0) and a radius of 1. Since the radius is one, the largest value of x is when y=0 and the largest value of y is when x=0. You can see a unit circle and they talk about the nature of Sine here: http://www.youtube.com/watch?v=JPWVnpdfa0E
We are primarily interested in the y axis since the will be opposite in the Sine formula of opposite/hypotenuse. From that graph, it’s pretty easy to see that the value of y is going to never be greater than 1 and never less than 0 for any angle between 0 and pi. Also, since y is always going to be less than the radius, it will be smaller than the hypotenuse which is the radius. A smaller number(x) divided by a bigger number 1(the radius) will be a fraction that is less than 1. However, it is possible for sin to be negative if the angles are greater than pi. At that point, y becomes negative which changes the sign of the result. The original problem was restricted between 0 and pi though, so that will not happen in the problem you stated.
You can see this in a table of sin values here:
http://www.grc.nasa.gov/WWW/k-12/airplane/tablsin.html
It should be easy to see from that table that it is never greater than one or less than zero.