(a)Intermediate Value Theorem is that when a function is continuous, we can pick a number c in a interval (a,b) and there exist f(c) in a interval (f(a), f(b))  . To make someone with no knowledge of the IVT, we can give an example like taking a plane from Australia to China. As is known to all, the earth is a sphere and there is no way for us to take a plane from Australia to China without crossing the equator. No matter how pilots arrange the air line, there exist a point that he has to cross the equator and that is as the same meaning of IVT, which we can definitely find a c in a interval (a,b) and make f(c) in a interval (f(a), f(b)) if this function is continuous.

Therefore, we can know what this question want to express. Since f(0) is smaller than 0 and f(pi) is greater than 0, there exist a point a in (0, pi) such that f(a)=0.

(b)My argument is relied explicitly on the concept of continuity.