Mathematics

Problem

On the interval

[0,2\pi]

, consider

f(x)=\sin x

and

g(x)=\dfrac{x}{\pi}

. Identify every subinterval of length

\dfrac{\pi}{2}

within

[0,2\pi]

for which an intersection of the graphs of

f

and

g

is guaranteed, and state how many such guaranteed intersections exist.