Question 121
A function
$$
f(x) = \cos x \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{3} \cdots \cos \frac{x}{2009}
$$
is defined on the segment $\left[0, \frac{2009\pi}{2}\right]$. Find the number of points at which this function changes its sign. (B. Trushin)
$$
f(x) = \cos x \cdot \cos \frac{x}{2} \cdot \cos \frac{x}{3} \cdots \cos \frac{x}{2009}
$$
is defined on the segment $\left[0, \frac{2009\pi}{2}\right]$. Find the number of points at which this function changes its sign. (B. Trushin)